Only a few. Polestar is technically Chinese (Geely owned, they bought out partner Volvo recently) but they wouldn't have a huge market share. There are probably a few others. BYD is building factories in Mexico, so there may be some imports from there in the next few years. Otherwise, the US has 25% import tariff on foreign cars and incentives for domestically produced cars. So, that's a huge price advantage for what are otherwise not very competitive American vehicles at this point. The export market for those is shrinking rapidly. There's a bit of a niche market for pointlessly large trucks in Europe. But it's tiny and they just aren't very practical or economical there. Things like F-150s, Rivian, Rams, etc. are extremely uncommon over here. Rivian might grow internationally with their new, smaller models. But otherwise, it's mostly Tesla, not a whole lot of Ford (their market share has vanished rapidly in the last years), and not much else succeeding abroad.

By the time Chinese manufacturers open (or more likely take over) factories in the US, they will already have a huge market share elsewhere. There's going to be no shortage of struggling US manufacturers looking for an acquisition in a few years. That's what happened to Chrysler after they went bankrupt. It's also a bit of a repeat of what happened with Japanese cars in the eighties.