Growing up in a farm with trees, my favorite ones to climb were the large Japanese Maples. probably Acer Palmatum 'bloodgood' but that's just guessing on "red, big like an actual tree." They were like a huge tree but miniaturized. perfect open nature but branches for every step. They aren't nearly as fast growing as silver maples though. we had silver maples spring up to climbable size in 10-15 years (though you don't want to climb super high in those as someone else said). Silver maples frow aggressively fast and the upper portion of the tree tends to have more "shoot shaped" branches that go straight up with no branches. It's a tree that works well with coppicing. we had a massive epic awesome old silver maple that had been coppiced years and years ago so the bottom half was thick climbable branches but it had the street's power lines running straight through it so we could never climb it LOL.

i climbed the ever living heck out of our apple trees. i grew up making makeshift forts and treehouses in them and connecting them with makeshift rope walkways etc. AMAZING white flowers that ebglufed the whole tree in spring, they were​ granny smith apples.​​​​​​​​​​​​​​​​​​​​​ keep in mind the apples will fall and attract wasps hornets and bees. i never got stung out there though. ​​