Yes. Much easier to do when limbs are thinner. But do it correctly. Even easier is to rub off buds before they even grow into branches.

For the look of the tree when it gets to full height should I wait or is it close to finished growing?

I would start now

It isn't remotely near its full height. Just prune to make mowing easier then leave it alone. Removing lower limbs will not affect its ultimate height. Which will be in a couple of centuries ...

I'd live with those branches for now. I think they do look better with the lowest branches 30 ft from the ground instead of 40.

As said earlier this is no a small tree, as in 20 to 30 years, you are looking at about 70' tall. If it were mine I would remove the lower branches to about 8 to 10' up from the ground. This will make it easier to mow and maintain the area under the tree. If you will notice the lower branches droop, so as the tree grows further you may need to cut an addition 4 of branches. You do not want an area under the tree where nothing will grow.

We have one that is about that height. It was a woods tree and was nearly branch-less for about 30 feet up the trunk. In the first 13 feet I did not leave any branches, but let the upper part do what it would.

15 years later the tree is getting a very nice shape. Branches are growing from the leaf buds that sprouted if that upper area and the tree is developing a very nice shape

Too late in the season to be pruning! Wait until late winter.

Great info. Thank you all!

Wow, that’s a very nice tree. I can’t help with pruning advice as I've never seen a Tulip with branches and foliage that low. Tulips are common in my neck of the woods (SE PA) - all of mine are growing in a wooded setting, they were here before me, and the first 20 to 40 feet is usually all trunk (first photo). The Tulip in the second photo was probably limbed by a Lenape dugout-canoe maker 😁 . Also, I can’t tell if your tree branches are close to the utility pole wires – if so, the ‘utility company’ may come along unannounced and prune the branches – usually not to ones liking.

They're not native here. This one is free standing in a park so branches come lower but still start about 20 feet up. Probably pruned up. Planted in the 18th century. Towers over the houses which are five storeys. Btw I'm sure you know it isn't a true poplar.

My word, trees get huge in England.