It’s “experience” and no, “big” doesn’t work as a substitute here. Big is more like size or importance such as, I had a big project I worked on.

“Big experience” would be rarely used, and would have a different meaning than “a lot of experience” which means that you have done a lot of something. You could say, perhaps, ‘Piloting the space shuttle was a big experience” meaning that it was something important to you. Though “important” is better than “big” here

As Andrea said, but in addition, you might say, in an informal context: "I had a great experience in the company I worked for last." In other words, you enjoyed it immensely.

Hi Mehrdad Big experience doesn't really sound right, "have a lot of" or "to have broad/extensive experience in.." are more widely used, at least in British English

Hi Mehrdad Big experience doesn't really sound right, "have a lot of" or "to have broad/extensive experience in.." are more widely used, at least in British English