25mm to 38mm is a pretty big jump. Do you have photos of the part of the frame where the tire is now? With a caliper measurement for scale?
Keep in mind you want some clearance- if the gap is say 40mm, you'll have 1mm of clearance both sides which is not enough. As far as I know, there's no hard and fast rule, but roughly 5mm each side seems to be a rule of thumb minimum.
Take it into your local bike shop. You'll pay a little more for the tyre than if you purchased online, but you'll have advice, different ones to try, and someone to do the hard work for you, with nicer tools. Plus you'll make a good contact and help put food on a local table.
For what it's worth, I run 32mm on my gravel bike, and that's seen some shit. You'd be fine with under 38mm for rail trails (and more).