The correct way is to frame the opening with a header, jack studs(aka trimmers) and king studs in the same manner that window and door openings are framed. See image below for reference.
The header is typically made of two pieces of 2x lumber face nailed together, sometimes with a piece of 1/2” plywood between the two to make the depth of the header match ...
That's an outside air intake. It's purpose is to allow air in but keep critters and debris from entering. They make these specifically for this purpose but a common use is to take a DRYER vent that has a screen, remove the flapper (which would prevent air from entering) and use that as the intake.
You should find either at your local home supply store.
This old house has an excellent video on why the soffit location can be bad, and how to put it through a common shingle roof instead:
How to Vent a Bath Fan Through the Roof, August 2014.
The problem with the soffit is depending on climate, warm air heading back up and causing mold under the roof sheathing. ...