The match between 134th ranked Ymer and 62nd ranked Altmaier was a tight one.
Ymer was the sharpest, could break one of the German's serve clips and won the first set 6-4.
In the second set, the mean went back and forth in time with the serve balls, all the way to the tiebreak.
There, Altmaier went up to 5-1 and looked to force a third decisive set.
But Elias Ymer got up, won six straight balls and took home the set and the match.
In the second round, Ymer will face 14th-ranked Diego Scwartzman from Argentina.
The match will be played on Wednesday, July 13, at 11 am.