Original RCT most definitely had underground building, both for paths and attractions. I think 1 or 2 parks in the 'campaign' was even centered about being mostly underground.
You could definitely build underground in the original game.
I only ever had the original one when growing up and did stuff underground a fair bit. One of the early campaign parks came with a bunch of rides and stuff underground off the bat.
I think there were some practical changes to make it a bit easier in RCT2, but it was never hard.