And anything capable of sending people to Mars, which the BFR is designed to do, could also send people to Toril. And getting off of Toril isn't as hard as you might think, though the US Government wouldn't plan for it, if you attach a Spelljamming Helm to the BFR spaceship, and get a magic using character to pilot it, it can go back into space without a lower stage. You could in fact take that spaceship into orbit with a full tank of fuel, and then you could be on your way back to Earth.
I have an idea for the Captain, his name is Michael Gordon, he is an Air Force pilot who transferred to the Space Force when it was formed. The spaceship was named the Hans Zarkov by Elon Musk, as a sort of reference to Flash Gordon, a sort of in-joke because the Captain's last name is Gordon. The Space Force bought the ship from SpaceX and kept the name. So basically it lands outside of Waterdeep, and there are some agents of other powers, such as Thay that are getting a little alarmed and may try something. I'm using the material in the module Dragon Horde as a source of materials and villains. Any ideas about what they might try, and how it might affect the crew and the ship? Some other powers might get jealous of Waterdeep's dealings with off-worlders, while there is magic, technology still matters, guns and such could alter the balance of power in the region.
The Mars is much more easy to reach when you wait for a good launch window, so no, just because something can reach Mars doesn't mean it would be able to reach Toril. And landing outside of a population centre would be monumentally stupid. You can't account for the reaction of the native, something might go wrong and you destroy the city and it is not even clear if the astronauts would be fit to actually interact with the natives in any way instead of needing to be hospitalized from the intense solar radiation.
Look, if you want a space opera then simply say so in the premise instead of asking what would happen if Toril appeared in the real world and then ignore all real world ramification because you want space fantasy.