The experience depends on which iPhone SE generation you own:
You cannot specifically pick an older version like 13.7 if your phone is eligible for a newer update; the Software Update menu will only offer the latest compatible version. Current Status for iPhone SE Models Download iOS 13.7 for iPhone SE
If your iPhone SE is already on a newer version (like iOS 14 or 15), you cannot revert to iOS 13.7. The experience depends on which iPhone SE generation
Because Apple no longer authenticates this software, you cannot install it even if you have the original firmware file. Why You Can't Download iOS 13.7 Download iOS 13.7 for iPhone SE
is currently impossible through official Apple channels. Apple stopped signing iOS 13.7 on , shortly after the release of iOS 14.