How to properly increment an int identity in SQL Server if the Identity Increment isn't set?
The best option is to use the SEQUENCE object, introduced in 2012. Since it is an independent object, you don't run the risk of querying it at the same time and retrieving the same value - it'll always provide the next in the chain.

Set the object with a specific start and increment value, then call it to get the next value desired. One of the biggest benefits here is that you can also specify a number of values to be cached for faster retrieval if you're working with rapid inserts.

CREATE SEQUENCE seq_obj
    START WITH 1050
    INCREMENT BY 1
    CACHE 1000
GO


Then to get the next ID value, use:

SELECT NEXT VALUE FOR seq_obj


Which will provide 1050, then 1051, and so on and so forth.

MS Docs for full information on other properties.