You don't need to have an account with ICICI or any bank to have a salary account. However, there are a few eligibility criteria (ICICI) which the company has to meet. They are:
1. The organization/company needs to have a minimum of 20 employees employed.
2. The total annual payout for the employees should not be less than 36,00,000/- INR.
3. The average salary should be 15,000/- INR per year.
Also, please be advised that you don't need an introducer/introduction to open a salary account.
In your case, I don't think you would be able to open a salary account with any bank until your employee strength reaches 20. As our fellow member Bhaskar mentioned, you can pay them through a cheque, which is also accounted for and would be useful in due diligence/audit.
Thank you.