Is there a Lazy Approach?

I just upgraded my 2012 MacMini. I replaced the internal HD with a SSD, and doubled the memory.

I did a Time Machine Backup to an external disk. I replaced the internal HD with a SSD. Did a clean install of Mojave. Then thought I loaded everything back to the new internal SSD from Time Machine. Booted up and none of the data was there and precious few Appls.

I guess I could re-install the old internal HD and copy everything to an external rather than using Time Machine. Then re-install the new internal SSD.

But I’m looking for a lazy man’s way out. Is there a way to retrieve the data on the old internal HD without having to re-install it?