You swallow your pride and you deal with the crap architecture and try to make the deadline.
Your boss hasn't got a problem with the architecture. You can try to convince him when there is less time pressure. But for now, you need to deliver what is considered the MVP to meet the deadline.
Businesses exist to make money. They don't exist to write good software.
Ultimately poor architecture will come back to bite. You need to figure out if you want to be around when that happens, if you can't convince your boss that things need to change.