I just looked it up on The Spruce website. It says to prune the lower branches in warm weather to create a canopy shape. I love those trees!

Is that Desert Museum? It looks like it and if its thornless that‘s likely what it is. We have two but they both very quickly grew to good sized trees from 15 gallon pots. pruning lower branches is a good idea as a lot of desert trees will be big bushes if you let them. Heres ours about 5 years from a six ft plant.

I think you should remove the stake, it could be girdling the tree and impeding its growth. Fill the hole left by the stake with soil.

If you choose not to remove the stake, at least remove the bright green tape and replace with something soft and unobtrusive such as hessian, sisal or jute.