The inflation adjusted cost of the moon program for 13 years was $19.76 billion per year in 2020 dollars.[1] At the time it was 4.4% of the federal budget.
I see absolutely no reason why, if they had not continued, they would have somehow needed 80% of GDP to set up a permanent base. It seems they got the entire moon program done for way, way less and indeed we ended up eventually building and keeping occupied the international space station. The additional effort to do the same thing on the moon would not somehow swallow all government expenditures.
I mean hell consider what we have spent on unnecessary wars and our inflated military budget. There absolutely could have been an alternate timeline where we were focused on space expansion and not purely military expansion.
[1] https://www.planetary.org/space-policy/cost-of-apollo
[2] https://www.cbsnews.com/news/apollo-11-moon-landing-how-much...