I would recommend contacting the seller ASAP as ask for an extension of the contract. Unless they have another buyer waiting in the wings, it does them no good to void the contract. Ask for something reasonable, perhaps another week. Hopefully by then you'll have your paycheck in hand.
If you have a signed contract that states your income, that might help. An offer letter, unfortunately, carries little weight, because it doesn't indicate that you've actually taken the job. I had this problem when I first started looking for homes - I took a job with a considerably higher salary, but until I actually had a paycheck, my loan officer said that it wouldn't be worth my effort to try to get approved for a loan. Even though my employer (the Federal government) has as establish employment and income verification system precisely to avoid these problems, it was not good enough for the underwriter. And this was back when loans were relatively easy to get.
Another thing that you could try is talk to whomever is in charge of distributing the paychecks. Often, your salary is disbursed a week after pay period ends - for example, if you work from August 1-14, you get your paycheck on August 21. If you've worked a full pay period, maybe your employer would be able to cut you a paycheck a few days earlier.