Can I apply for a 60-day visa before doing a border run in Thailand?

No and you won't get 60 days with a border run, a border run will get you 30 days.You'll have to exit Thailand, on what's known as a visa run, and visit a Thai consulate in which ever country you exit to and apply for a tourist visa to get the 60 days you desire

If you’re thinking of using the evisa system whilst in Thailand it won’t work for you. The embassy the application routes to will want to see proof that you’re in that country and that you’ll be travelling from there to Thailand with flights etc.

To get an actual 60 day visa you’d need to apply at one of the nearby consulates in person. None use the evisa system. You’d need to check their website for requirements.

If you do a border run and then get an extension you will get 60 days anyway

You cannot get a tourist visa while you're inside Thailand.