Purdue started playing baseball back in 1888.
The NCAA started having a baseball tournament in 1947.
Like in basketball, the first year was an 8-team single elimination tournament won by California over Yale. As a fun footnote, some guy named George H.W. Bush played for that Yale team.
Through all 71 years of the NCAA Tournament, Purdue has been eligible to participate, but unlike in basketball, we have virtually no history in it. Since the early 70s baseball has been dominated by Southern and Western schools that can play year round. For a long time they could start playing games in mid-January, while schools like Purdue would have to go on the road entirely until mid-March at best.