, You should have plenty of time if you start researching the requirements for paperwork now.
Getting the background check (and related notaries/authentication, if required based on your list from the Thai Consulate in your area), bank letter and corroborating financial statements, and medical tests (some doctors will want to do blood tests) are the things you'll need at least 2 weeks lead time for, conservatively. The rest tends to be easier (like getting copies of passport photos, filing out forms, etc.). Timing for getting the actual visa depends on whether you go into your region's Thai Consulate office or send passports in via the mail.
**Just make sure you are following the timing they require (getting the visa and various documents signed no more than so many days before leaving, etc.).
My husband and I just went through this for our Non-Immigrant O-A visas and it took us 1 month to get everything together. We went in to the Thai Consulate in our region and that was a 2-day process based on the website guidelines. Good luck! It was much easier than I thought once we got clear about what was required and made a checklist we could follow with all the guidelines/dates to stay on track.