This is not normal for international students and you need to contact the Immigration team at your prospective university for their advice. It's recommended for UKVI that you submit your visa application as early as possible, which is 3 months before the start date. One month is not going to be long enough to get your CAS, get a confirmed offer, submit your visa application, attend a biometric appointment, and wait for the outcome of the visa assessment. There may be a week or more between each step. And even if you pay a lot of money for priority visa service, you should expect it to take 3 months. UKVI is notorious for being slow and making mistakes.
It's likely you'll need some kind of special consideration by the university to get your CAS information before your final grades and thesis are done, otherwise you'll have to start later.
