Mounting a scope without drilling holes?

Duck tape

Don’t scope it. Maybe go with a peep site.

That bracket still has to be screwed to barrel
If the barrel doesn’t have a groove for the mount to fit. .... you’ll have to drill holes.
Have the same bracket on an old Remington 22. Works fine

Wasn't sure if there were existing screw on the side of the action that the bracket could be mounted to...

Yeah there’s no holes or anything to mount a bracket like that to. I was thinking would loctite or something similar have enough hold?

Silver solder would probably do it. That's how they attach vent ribs on shotguns. You will have to find a base that has the same contour as the receiver. Silver solder doesn't like wide gaps. If you ever wanted to get rid of it, silver solder will release under heat and what is left could be sanded off. Only problem would be you will lose your original finish.

I'm sure there's an epoxy that will probably hold a mount on a .22 also. I would recommend a steel base as opposed to aluminum. The reason being that steel and aluminum have a different rate of thermal growth. So when the metal gets hot or cold, the differential thermal growth will put an epoxy in shear stress and may cause it to fail. Epoxies can handle a tensile load pretty well, but shear load, not so much. Again, to completely remove the epoxy would probably require some sanding.

Honestly, if the receiver is thick enough, I don't know why drilling and tapping wouldn't be the best way to go. You can install filler screws if you want to go back to original sights.