All we have to do is make the global religion require bringing a rock to a specific location; after long enough we’ll have a mountain so high it extends out of the atmosphere!
Aye man, wey aye, went doon there worra bairn, didn’t ah? Cannae remember much like, was only a wee nipper at the time, knaa what ah mean? Me mam an’ da took us doon the Toon when ah was nowt but a little’un, like. Divvent really remember owt aboot it proper, but aye, been the once when ah was just a littl’ bairn, me. Proper yonks ago that was, pet!
Related and recommended: Greg Egan “Phoresis” a sci-fi novel of two twin planets in extreme proximity to each other. (I think I read it in one of his anthologies.)
To get to the Kármán line (100k) a mountain with a 60 degree slope would require a base of 115km. A cone with 115km diameter base has a volume of 3.5×10^5 km^3. Which is 3.5x10^14 m^3, which is about 10^15 kg of rock. So it is going to take you a while!