Could cut it probably but this isn't a private company we are talking about here. The regulations and grifting would be massive, especially in New York which is quite like California with their wastefulness: half to the garbage can, half to their pockets, maybe a cent or two for the actual rails.
So maybe it'd be a few billion at least. Not to say they shouldn't try. But I expect it'll be over budget and behind schedule, it would never happen like Brightline where they broke ground ASAP and just kept building until it was done.
I don't share your pessimism, and that's mostly because I've followed a lot more of the research into why US infrastructure costs are unreasonably high. To put it simply, excessive costs tends to come from a combination of overdesign (in particular the need to add lots of goodies to buy off stakeholders who can otherwise arrest the project), extra overhead in design costs, extra overhead in the way contracts are let, and incompetent management of contractors. But this is the sort of project that doesn't have the design stages to let that scope creep come in--it is pretty much "order off-the-shelf part number 42341 instead of 23421, then do routine maintenance tasks to replace old parts with new ones".
So maybe it'd be a few billion at least. Not to say they shouldn't try. But I expect it'll be over budget and behind schedule, it would never happen like Brightline where they broke ground ASAP and just kept building until it was done.