I think most folks here would be sympathetic to your plight. Mine came off while driving (don't ask) and I tried for a few moments to pop it back on. No chance. Even after stopping, it took a minute or two figure out the 'engineering'.
If memory serves, you have to rotate the mirror relative to the base as far as possible and push. It helps to swivel the mirror so you can rotate its base as far as possible without hitting the headliner. Make sense? I hope so. Welcome.
Give it a try,
Dave M