In the absence of a background verification process, the appointment letter can be issued once the candidate has accepted the job offer verbally or via email. This is typically done after the final interview and salary negotiation.
Regarding the date to be mentioned in the appointment letter, it should be the date when the employee is expected to start working. This is known as the joining date. Even if the letter is issued after the joining date, the mentioned date should still be the original joining date. This is important for calculating the employee's tenure, benefits, and other related aspects.
However, it's worth noting that not conducting a background check can pose potential risks to the company. It's advisable to consider implementing a background verification process to ensure the credibility of the new hires. This process can help verify the candidate's employment history, educational qualifications, and any potential criminal records. This could be crucial in maintaining the integrity and safety of your workplace.