If you're in the US, you can certainly give a 1 month notice, but your employer can choose to accept it immediately or at any time ahead of the stated date.
If you're resigning, it's essential that you give a fair amount of notice to your company. The standard time to give a company is two weeks to one month, but it can vary depending on the type of job.
While you may not be legally required to give notice, most employers expect a notice of two weeks or more to help them reassign your responsibilities and hire a new employee.
I am writing to formally acknowledge receipt of your resignation notice on date. As you requested, your final day of work at Company Name will be end date. It is with great regret that we see you go. It has been a pleasure working with you these past X years, and we appreciate your contribution to the company.
Dear Manager's name, I'm formally tendering my resignation as current job title at company name. I would like to start my two-weeks / one month notice process today. My last working day with the company will be on dd/mm/yy.
Failing to work your notice period when it is contractually required can put you in breach of contract. While it's uncommon for employers to take legal action in such cases, it is within their rights to do so.
There's no rule against quitting a job after a month. If you quickly realize the job isn't a suitable long-term fit, resigning will actually help your manager find an employee that's better for the role.
Make a formal statement of acceptance Include a formal statement that you accept the offered position and agree to the terms of employment listed in the offer letter. Be sure to include the job title in your statement. You can also make specific mention of some of the important terms like compensation and start date.