Your browser and/or OS has a list of trusted certs called "certificate authorities". When it receives a cert from a web site, it checks that it was signed by a CA. So what you're asking is to become your own CA.

That basically means convincing Mozilla, Microsoft, Google, Apple, etc. that you know how to safely manage certs. It tends to be a pretty high bar. For example, many CAs have a root cert that they keep locked away in a safe that only a few people have access to behind several other layers of security. They have a secondary key that's signed by the root, and the secondary key is used to sign actual customer certificates. That way, they can expire the secondary every year or so and only ever use the root when they need a new secondary. IIRC, Let's Encrypt has two secondaries with overlapping expiration times.

So to answer your question, no, not unless you're willing to go to great lengths and have a great deal of knowledge about TLS.

I don't know what the process is like to become a certificate authority. I imagine the answer is technically yes but realistically no, at least not as an individual. You'd be providing a critical piece of internet infrastructure, so you'd need the world to consider you capable of providing the service reliably while also capable of securing the keys used to sign certificates so they can't be forged. It's a big responsibility that involves putting a LOT of trust in the authority, so I don't think it's taken very lightly.

Sure, just convince the creators and maintainers of important software certificate stores to add your trust root. For example: Google, Mozilla, Microsoft, Apple, Linux, Cisco, Oracle, Java, Visa.