In 1993, John Olerud hit .400 as late as August 2, as his Retrosheet game log shows. By comparison, that same year Andres Galarraga was hitting .400 as late as July 5. They are, so far as I know, the two hitters from 1990 onward to get to .400 after June of a given season. You might think Tony Gwynn got there in 1994, since he hit .394 in that shortened season-but, he peaked at .400 on May 15.
The window for someone to achieve a .400 batting average opened quite a bit in the ’90s and 2000s with the general offensive surge in those decades, but now seems to have closed, or at least narrowed to a crack.