Short answer: President, unequivocally no. Local office, yeah, and not as hard as you might think.

President has pretty open formal requirements, but the informal ones are the killer. To be on the ballot, you need to get a threshold of signatures that varies by state, so you need to fund a campaign well enough to attract enough people to go out and stand on street corners or go door to door collecting signatures in all 50 states. That's tens of millions of dollars you'd need to raise just to be on the ballot. Then you've got the actual campaign and unless you're running with a major party, you would need to raise it all by yourself. The last presidential race cost billions of dollars, so without a political party's support, which you won't get because you're an outsider, you'd better be friends with some billionaires and prepare to sell off huge chunks of your authority to get elected.

Local elections, especially things like city council are reletively easy. You need some signs, flyers, a website, and good campaign strategy. All of that costs money but you'll need to gather the support of local business owners or residents and solicit campaign contributes, maybe $20k for a small city. If you're in a bigger city the money you need to raise goes up and so does the presence of crony politics like in the presidential races, but unless you're criminal record was rape, selling drugs, or murder, the background won't matter.