Not necessarily. NASA needs to start building the Gateway before the SLS is ready, which won’t be for a while. Falcon Heavy is the most powerful rocket in existence right now.
The rockets are fine, but they had better do some serious research to make sure the Gateway can handle all kinds of space radiation and other dangers (from all over the electro-magnetic spectrum) of a _long-term_ orbiting system around the moon.
There will not be _any_ atmosphere to protect it, so this is _totally_ untested technology.