I got a job after my Masters, and worked there for 10 months. I had some issues with my supervisor so I left the place without giving proper notice. Naturally, I did not get the Experience Letter from the company. After 11 months, I got another job at a small firm where 10 people worked. They did not insist on the prior Experience Letter. I worked there for 10 months and then got another job. They only asked for the latest Experience Letter which I did have.
However, I think lately the background checks have become stricter, and I recently lost an amazing job opportunity due to not being able to produce the Experience Letter from my first job.
Obviously, I cannot show the first job on my resume since background check requires the relevant Experience Letter. As a result, I now have to show nearly 2 years gap after my Masters (10 months of employment at the first company followed by 11 months of unemployment).
I have nearly 4 years of continuous work experience. What explanation could I give for the gap of 2 years?