I recall seeing a 1943 Ashburn's map that had that area marked "polo grounds". I have also seen a 1953 issue of This Month in Fort Worth with a photograph of those apartments calling them "new". My memories are subject to revision by the passing years, of course.
The theater in the photograph is south of the T&P tracks, between them and Rosedale/Tension and wedged against the underpass, which is to the east. The screen faces south or southeast. I'll bet it was mighty entertaining for moviegoers when trains went by.
I once noticed on each side of the underpass plaques by the TX highway dept. indicating that it had been built in, I think, 1942. Or '43. WW2, anyway.
One thing you can do now is go to the library and look in the city directory for the year it was built and learn the name of the first occupant. Then you can learn his occupation and his spouse's name.
I'm not sure but directories from that long ago may be on microfiche. It would be nice if all of them could be made digital.
When travelling to and from the house, the Kellys always took New York Ave, which was unpaved, and avoided paved Evans Ave, knowing that the laws watched the paved streets but ignored the unpaved ones.
Now, who knows Machine Gun's real name, and how did he come by his Tommy gun?