Finding all joins required to programmatically join a table
I had a script that does a rudimentary version of foreign key traversal.  I adapted it quickly (see below), and you might be able to use it as a starting point.

Given a target table, the script attempts to print the join string for the shortest path (or one of them in the case of ties) for all possible source tables such that single-column foreign keys can be traversed to reach the target table.  The script seems to be working well on the database with a couple thousand tables and many FK connections that I tried it on.

As others mention in the comments, you'd need to make this more complex if you need to handle multi-column foreign keys.  Also, please be aware that this is not by any means production-ready, fully-tested code.  Hope it's a helpful starting point if you do decide to build out this functionality!

-- Drop temp tables that will be used below
IF OBJECT_ID('tempdb..#paths') IS NOT NULL
    DROP TABLE #paths
GO
IF OBJECT_ID('tempdb..#shortestPaths') IS NOT NULL
    DROP TABLE #shortestPaths
GO

-- The table (e.g. "TargetTable") to start from (or end at, depending on your point of view)
DECLARE @targetObjectName SYSNAME = 'TargetTable'

-- Identify all paths from TargetTable to any other table on the database,
-- counting all single-column foreign keys as a valid connection from one table to the next
;WITH singleColumnFkColumns AS (
    -- We limit the scope of this exercise to single column foreign keys
    -- We explicitly filter out any multi-column foreign keys to ensure that they aren't misinterpreted below
    SELECT fk1.*
    FROM sys.foreign_key_columns fk1
    LEFT JOIN sys.foreign_key_columns fk2 ON fk2.constraint_object_id = fk1.constraint_object_id AND fk2.constraint_column_id = 2
    WHERE fk1.constraint_column_id = 1
        AND fk2.constraint_object_id IS NULL
)
, parentCTE AS (
    -- Base case: Find all outgoing (pointing into another table) foreign keys for the specified table
    SELECT 
        p.object_id AS ParentId
        ,OBJECT_SCHEMA_NAME(p.object_id) + '.' + p.name AS ParentTable
        ,pc.column_id AS ParentColumnId
        ,pc.name AS ParentColumn
        ,r.object_id AS ChildId
        ,OBJECT_SCHEMA_NAME(r.object_id) + '.' + r.name AS ChildTable
        ,rc.column_id AS ChildColumnId
        ,rc.name AS ChildColumn
        ,1 AS depth
        -- Maintain the full traversal path that has been taken thus far
        -- We use "," to delimit each table, and each entry then has a
        -- "&lt;object_id&gt;_&lt;parent_column_id&gt;_&lt;child_column_id&gt;" format
        ,   ',' + CONVERT(VARCHAR(MAX), p.object_id) + '_NULL_' + CONVERT(VARCHAR(MAX), pc.column_id) +
            ',' + CONVERT(VARCHAR(MAX), r.object_id) + '_' + CONVERT(VARCHAR(MAX), pc.column_id) + '_' + CONVERT(VARCHAR(MAX), rc.column_id) AS TraversalPath
    FROM sys.foreign_key_columns fk
    JOIN sys.columns pc ON pc.object_id = fk.parent_object_id AND pc.column_id = fk.parent_column_id 
    JOIN sys.columns rc ON rc.object_id = fk.referenced_object_id AND rc.column_id = fk.referenced_column_id
    JOIN sys.tables p ON p.object_id = fk.parent_object_id
    JOIN sys.tables r ON r.object_id = fk.referenced_object_id
    WHERE fk.parent_object_id = OBJECT_ID(@targetObjectName)
        AND p.object_id &lt;&gt; r.object_id -- Ignore FKs from one column in the table to another

    UNION ALL

    -- Recursive case: Find all outgoing foreign keys for all tables
    -- on the current fringe of the recursion
    SELECT 
        p.object_id AS ParentId
        ,OBJECT_SCHEMA_NAME(p.object_id) + '.' + p.name AS ParentTable
        ,pc.column_id AS ParentColumnId
        ,pc.name AS ParentColumn
        ,r.object_id AS ChildId
        ,OBJECT_SCHEMA_NAME(r.object_id) + '.' + r.name AS ChildTable
        ,rc.column_id AS ChildColumnId
        ,rc.name AS ChildColumn
        ,cte.depth + 1 AS depth
        ,cte.TraversalPath + ',' + CONVERT(VARCHAR(MAX), r.object_id) + '_' + CONVERT(VARCHAR(MAX), pc.column_id) + '_' + CONVERT(VARCHAR(MAX), rc.column_id) AS TraversalPath
    FROM parentCTE cte
    JOIN singleColumnFkColumns fk
        ON fk.parent_object_id = cte.ChildId
        -- Optionally consider only a traversal of the same foreign key
        -- With this commented out, we can reach table A via column A1
        -- and leave table A via column A2.  If uncommented, we can only
        -- enter and leave a table via the same column
        --AND fk.parent_column_id = cte.ChildColumnId
    JOIN sys.columns pc ON pc.object_id = fk.parent_object_id AND pc.column_id = fk.parent_column_id 
    JOIN sys.columns rc ON rc.object_id = fk.referenced_object_id AND rc.column_id = fk.referenced_column_id
    JOIN sys.tables p ON p.object_id = fk.parent_object_id
    JOIN sys.tables r ON r.object_id = fk.referenced_object_id
    WHERE p.object_id &lt;&gt; r.object_id -- Ignore FKs from one column in the table to another
        -- If our path has already taken us to this table, avoid the cycle that would be created by returning to the same table
        AND cte.TraversalPath NOT LIKE ('%_' + CONVERT(VARCHAR(MAX), r.object_id) + '%')
)
SELECT *
INTO #paths
FROM parentCTE
ORDER BY depth, ParentTable, ChildTable
GO

-- For each distinct table that can be reached by traversing foreign keys,
-- record the shortest path to that table (or one of the shortest paths in
-- case there are multiple paths of the same length)
SELECT *
INTO #shortestPaths
FROM (
    SELECT *, ROW_NUMBER() OVER (PARTITION BY ChildTable ORDER BY depth ASC) AS rankToThisChild
    FROM #paths
) x
WHERE rankToThisChild = 1
ORDER BY ChildTable
GO

-- Traverse the shortest path, starting from the source the full path and working backwards,
-- building up the desired join string as we go
WITH joinCTE AS (
    -- Base case: Start with the from clause to the child table at the end of the traversal
    -- Note that the first step of the recursion will re-process this same row, but adding
    -- the ParentTable =&gt; ChildTable join
    SELECT p.ChildTable
        , p.TraversalPath AS ParentTraversalPath
        , NULL AS depth
        , CONVERT(VARCHAR(MAX), 'FROM ' + p.ChildTable + ' t' + CONVERT(VARCHAR(MAX), p.depth+1)) AS JoinString
    FROM #shortestPaths p

    UNION ALL

    -- Recursive case: Process the ParentTable =&gt; ChildTable join, then recurse to the
    -- previous table in the full traversal.  We'll end once we reach the root and the
    -- "ParentTraversalPath" is the empty string
    SELECT cte.ChildTable
        , REPLACE(p.TraversalPath, ',' + CONVERT(VARCHAR, p.ChildId) + '_' + CONVERT(VARCHAR, p.ParentColumnId)+ '_' + CONVERT(VARCHAR, p.ChildColumnId), '') AS TraversalPath
        , p.depth
        , cte.JoinString + '
' + CONVERT(VARCHAR(MAX), 'JOIN ' + p.ParentTable + ' t' + CONVERT(VARCHAR(MAX), p.depth) + ' ON t' + CONVERT(VARCHAR(MAX), p.depth) + '.' + p.ParentColumn + ' = t' + CONVERT(VARCHAR(MAX), p.depth+1) + '.' + p.ChildColumn) AS JoinString
    FROM joinCTE cte
    JOIN #paths p
        ON p.TraversalPath = cte.ParentTraversalPath
)
-- Select only the fully built strings that end at the root of the traversal
-- (which should always be the specific table name, e.g. "TargetTable")
SELECT ChildTable, 'SELECT TOP 100 * 
' +JoinString
FROM joinCTE
WHERE depth = 1
ORDER BY ChildTable
GO