Will an acute ear infection in an adult with an avarage immune system cause meningitis?

Unlikely: But in some rare cases, if not treated or if dealing with a resistant bug, it can cause it.

No: A middle ear infection, otitis media, is a simple localized infection. It is often caused by a virus and will resolve spontaneously. Otitis media can be caused by bacteria and is easily treated with a 5 to 10 day course of oral antibiotics. The ear pain often improves dramatically in the first day. You can trust that your immune system safeguards your brain and body from this kind of infection.

Yes: But the difference between 'can' and 'will' can be enormous. Anything can happen, although in this instance it is exceptionally unlikely. If you have an ear infection it is likely viral, and using a decongestant may be of benefit. Meningitis seldom occurs from otitis in adults.

Maybe: If the infecting agent is aggressive and the host (you) is vulnerable, the ear infection could spread to the meninges. This is usually through hematogenous spread (through the blood stream) rather than through neighboring invasion. More common in kids. Rarely, if the infection is ignored, it can spread to the mastoid air sacs, thence to the venous sinuses in the brain, and thus cerebritis.

Very rare: It would be a rare occurrence.

Extremely unlikely: Even though theoretically, severe and chronic ear infection involving bone erosion leading to brain involvement, I have yet heard of one. As for acute ear infection, the risk is likely zero.