Can I Join a New Job Without Mentioning My Brief Stint at a Previous Company?

I have left a company after completing one month. I need to draft a formal resignation letter. I haven't signed any offer or appointment letter, so there is no question of serving a notice period. Can I join another company by submitting my previous company's payslip and relieving letter without mentioning my experience in this company?

It doesn't appear that you require any assistance to draft a resignation letter. As for your effort to conceal your current employment, it is a risk you are carrying and is also unethical. If you are going for a formal resignation, what stops you from taking due credit for it remains an enigma.