You can submit whatever proof you have including relieving order related to your work experience between 2018 - 2020 which is the maximum you can do.
The BGV should be limited to your past employment details only and really I don't understand the purpose behind asking GST no.
Are they planning to hire you or are they going to purchase your old company?
Any Vendor having business transaction with employer will be requiring GST no.
It is not mandatory for your past employer to provide GST no for employment verification.
Based on available information if they hire you, it would be well and good. If not look for other employer.
From India, Madras
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