There is no average time you can expect to receive a first offer. It all depends on the details of your crash and the insurance company handling your claim, among other things.
You may receive a settlement offer within a few weeks after your accident. While this may seem fast, that's the point – many car insurance companies strive to work expeditiously. In other situations, getting a settlement offer from the insurer may take a month or two.
Regardless of how long it takes to get your first offer, review the offer with a lawyer to ensure it meets your needs before committing.