Can I install Garage Band on MacBook Air running Catalina?

You would have had to already purchased an earlier, pre-Big Sur compatible version in the past.

The following Apple Support document describes how to redownload previously purchased apps, with emphasis on the re in redownload: Redownload apps and games from Apple - Apple Support.

"Learn what to do if you can't redownload the app."

Although I have never heard of anyone successfully doing so, or even attempting it, you have nothing to lose by contacting Apple. Beg, plead, or cajole them into make an earlier version available by supplying you a download code or something like that. But that's the only way it could possibly happen because Apple is the sole source for their apps. Don't let me stop you from trying though.

Only if you purchased an earlier version in the past. If so you can find it under Purchased.

What you need is GB version 10.3.5 or earlier.

What John meant was if you had downloaded GarageBand previously.