If I made an offer on a house but found out that the house doesn’t have a permit for a converted garage, can I withdraw the offer?

As to repairs: that only gives you a right to withdraw if the contract contained an "inspection contingency" or similar clause or provision giving you the right to terminate the transaction if you find damage or a need for repairs. If there is such a provision, then you can withdraw according to what it says--generally, such provisions require you to give the seller a chance to make the repairs, but that's simply what they generally say: you need to follow what the term in *your* contract says.
As to the converted room: that very likely will allow you out of the contract IF the seller cannot, quickly correct the deficiency and get the permit. If only problem, for example, was a lack of a final inspection, failure to pay some permitting cost, or failure to turn in some final paperwork and the seller now can do that, then the lack of a permit is not a "material" breach of the contract or fraud because the problem can be and will be corrected.
But if the problem cannot be corrected at all (it's simply illegal) or can't be reasonably corrected before the closing date (e.g. the room would have to be extensively rebuilt to code, permits applied for, etc., all of which will take a great deal of time), then you should be able to get out of the contract on two different theories:
1) Material (or important) breach of contract: you agreed to buy a home with a certain number of rooms--but the home is lacking one (an illegal room doesn't count).
2) Fraud: the seller represented that he could sell you a home with certain number of rooms, and implicitly represented that everything was legal (unless stated specifically to the contrary, home sales are always with the implicit representation that all rooms, renovations, etc. are permitted) but that representation was false.