Do we have to wait? Falcon Heavy already has ~75% of SLS Block 1's payload capacity (to LEO). For the $11.2 Billion that's earmarked for the next 4 years of SLS, you could buy 112 Falcon Heavy launces--one every ~17 days for four years. In contrast, the wiki lists a single planned flight for SLS during that period.
It's cheaper to buy, for sure. But we don't know the costs. It's possible that these launches are far less expensive than SLS, but equally unsustainable.
How might that be? SpaceX doesn't have to manufacture whole new rockets for every Falcon Heavy launch, but even if they did, as far back as 2016 they could build 16 new cores (5 Falcon Heavy's worth) per year.