You have time if the child isn't born yet. They won't be climbing shit for their first year at least, but after that things will get a little bit crazy. I've been lucky with my toddler, he's generally pretty good about climbing soft and comfortable things like couches, rather than clambering up ladders or cat trees.

You'll need a strap or bracket as high as possible that can fix one of the top platforms to the wall. Depends on the tree and how you have it oriented. You might be able to use something like a metal L bracket if you're close enough to the wall.

Try to find a wall stud to anchor the bracket if possible, it will always be your best bet. You can use a number of anchors, but if the kid goes really nuts and does something particularly stupid, they might just pull an anchor out of the wall or break the wall.

This kind of thing is particularly handy when you need flexibility very strong and comes long enough that you have a lot of options.