You have already filed your claim for benefits, right? If not, do so immediately. You will, of course, explain to the claims taker that you had no prior warnings, that you did not know your job was in jeopardy, that you had never been written up or told that you were being tardy for work too many times. You might want to mention the usual practice of the worksite, in other words, did you come in noticeably later than everyone else, or did people trickle in at their own pace. Was there a policy for calling in or using petty leave when one was late for work? Had anything ever been said to you about this issue?
After taking your claim, and getting your statement about why you are no longer working, the office will contact your former employer and get their side of the story about why you were terminated. When someone is terminated, to keep them from receiving benefits, the employer must show they had a good job related misconduct reason to terminate the person. This means they had to prove you did something voluntarily, knowing your job was in jeopardy, to cause you to be terminated. If you had no prior warnings or disciplinary trail for this issue, it has to be gross misconduct, something so bad you should not have done it, even one time. This could be something generally bad, such as punching out a co worker, or it could be something that has been listed in their handbook as immediate grounds for termination, such as looking up a personal website on their computer system or parking in the wrong parking area.
If they do not have this,and you are saying you made a good faith effort to do your job and did not realize you were in danger of termination, your chances of being approved for benefits are pretty strong. If they have documentation of where you were warned about violations of a fixed "manager conduct policy" whatever that is, then your chances aren't so good.
Once you have filed, you will be making certifications for the weeks as they pass. If your claim is approved by decision, you will eventually be back paid for each week you have certified since filing the claim, which will be several. Otherwise, you won't be.