iTunes Store Download songs

. . . .without having to sign up for the 'Try it Free' subscription?

Yes it is possible.

Don't tap Apple Music

Tap Music (from the Dock)

Next, tap iTunes Store, then tap in the search field and search. . .

Click an Album then tap Preview All to listen.

Then click Buy if you want to buy.

You need to tap iTunes Store and search in iTunes Store, don't tap Apple Music.

See again what posted.

If you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.