If you don't want to subscribe to Apple Music, you can still sync your purchases between your Mac and iPhone.
If you've downloaded these songs through iTunes, you can redownload your songs using the iTunes Store app on your iPhone. Open the iTunes Store app, then tap ..., then Purchased, and you can download any songs you've purchased through iTunes if you're signed into the same Apple ID.
Redownload music - Apple Support
If you ripped these songs from CD or downloaded music from another source, you can still sync your Mac to your iPhone the old-fashioned way. Connect your iPhone to your Mac with a Lightning to USB cable, and your phone should appear in the Finder sidebar. In the button bar, click Music, then choose the songs you'd like to sync to your phone.
Sync music between your Mac and iPhone or iPad - Apple Support
Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support
If your Mac has macOS Mojave 10.14 or earlier, your phone won't show up in Finder, but you can still sync your Music using iTunes. The process should be very similar, but your phone will show up in the iTunes sidebar rather than the Finder sidebar.
Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support