We do need a bit more information to help.
Birth dates of each person in your 2xGreat GM’s line.
The cM of the DNA match.
The match should have other matches who you both Share, it is very unusual not to have any Shared Matches. That said Ancestry only shows Shared Matches where the share is 20cM or greater, unless you subscribe to Pro Tools when you can see Shared Matches of low cM matches.
Thrulines accuracy can vary from 100% to 0%, you have to look at each individual in the proposed line and determine the accuracy of each one. They are, for want of a better expression, “cobbled together” from the trees that are on Ancestry and we know how inaccurate they can be.
I do not follow what you are writing that Ancestry is predicting, a DNA match is your 2x Great Grandfather as the likelyhood of that is that he was born c1900. My own 2xGGF’s were born in the mid 1800’s.
DNA is very accurate at determining actual biological relationships, questionable with very low cM, but above 20cM you can be confident that you are biologically related.