Because this enterprise has violated several provisions of the People's Republic of China (PRC) Labor Contract Law, as long as you confirm the evidence of your working time in this unit, your arbitration request will definitely be realized. Some rogue enterprises will deny that you work in this unit, and if you don't keep relevant evidence, you may not meet the arbitration requirements.
If you still have questions, you can call Tianjin Labor and Social Security Service Hotline 12333 during working hours on weekdays, and you will get a satisfactory answer.
The following are some chapters of the Labor Contract Law:
Article 82 If an employer fails to conclude a written labor contract with the employee for more than one month but less than one year from the date of employment, it shall pay the employee twice the monthly salary. Where an employing unit violates the provisions of this Law and fails to conclude an open-ended labor contract with the laborer, it shall pay the laborer twice the salary every month from the date when the open-ended labor contract should be concluded.
Supplement: Arbitration claims, like litigation, are based on evidence. The witness in your case is of course important, but some enterprises will overturn your witness. You should be fully prepared, and electronic attendance can certainly be used as evidence. Besides, didn't you have any information such as working documents signed by you during your work in the company?
Once again: as long as your working date (time) in this company is determined, the probability of winning all your (arbitration) cases is 100%, otherwise, as you said, the evidence of two months will only win in two months, unless the original unit does not object to your working hours.