Why is an aggregate query significantly faster with a GROUP BY clause than without one?
It looks like it is probably following an index on CreatedDate in order from lowest to highest and doing lookups to evaluate the SomeIndexedValue = 1 predicate.

When it finds the first matching row it is done, but it may well be doing many more lookups than it expects before it finds such a row (it assumes the rows matching the predicate are randomly distributed according to date.)

See my answer here for a similar issue

The ideal index for this query would be one on SomeIndexedValue, CreatedDate. Assuming that you can't add that or at least make your existing index on SomeIndexedValue cover CreatedDate as an included column then you could try rewriting the query as follows

SELECT MIN(DATEADD(DAY, 0, CreatedDate)) AS CreatedDate
FROM MyTable
WHERE SomeIndexedValue = 1


to prevent it from using that particular plan.