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DNA doesn't tell you who a person is without having a sample from a person to compare it to... We'd be able to tell if they were human or not. That's about it.
Not only that, but afaik there isn't just 1 body interred there. It's a whole mess of unidentified bodies buried together.
If you had access to a large genetic database, it would theoretically be possible to find living relatives, provided at least one (even quite distant) relative is included in that database. It may be possible to then retrace familial history to determine who specifically it may have been.
That’s more or less how they managed to find the Golden State Killer. Someone noticed that the GSK’s DNA had distantly related DNA listed in GEDmatch’s private database and family trees were constructed to narrow down suspects until only one remained based on timing, location, and other details. The person listed in the database and the GSK were so distantly related that they only shared a great-great-great-great grandfather.
And the gender. And whether they had chromosomal anomalies
Unless there was a serious mixup, we already know the soldier was one of four randomly selected males.