Kick the ball upstairs immediately
You have a project that is going to fail. You don't have any way of solving this.
If you just tried various things and let the three months pass, you will end up with an angry customer and angry bosses.
Instead contact the person/people who can actually solve the problem, while there is still time to act. Who that is depends on the organization.
At that level, they can
- increase your resources,
- shrink the scope, or
- extend the time limit.
The last two involves talking to the customer too.
Make a presentation that briefly outlines these solutions and ask them to choose one (or a combination)
Now, it is possible that the bosses refuse to listen and keep insisting on the impossible. This leaves it up to you to choose the least painful way for the project to fail.
You cannot magic up extra resources, so that is out.
You can shrink the scope. The customer will not get all of what they want, but they will get something to tide them over until you have the whole thing ready.
You can also extend the time limit. If the product isn't finished, then it isn't finished. So sorry.
Which of these is the lesser evil depends on the details of the project. Is it possible to create a "half-product" within the time limit? Will the "half-product" be useful to the customer? If both of these are true, go for the scope shrink, otherwise deliver late.