Read the offer letter again, find out what you signed.
Did the offer letter say anything like your salary will be guranteed for the coming 365 days? (I guess not)
Did the offer letter say the job is "At will"? (I guess Yes)
Your singning the letter just means you are going to take the job, it doesn't mean you can't change your idea.
The real job security is your skill. Even you start the work, you can quit anytime, the company can let you go anytime.
You need take care of your self and your family, chose the best offer for you. Nothing to worry about.