1. If you don't want to dig your hinge post into the ground, a DRIVEN post will be much more rigid than a dug and tamped post.
2. Use a post at least 10' long, and bury a whole lot more post in the ground.
3. The majority of the "problem" with the post sagging is going to come at the surface ground area, NOT from the part buried deeper in the ground.... so there's three or four things you can do for that....
a. If your concern is only for it sagging in the direction when closed, bury a second post up against the hinge post, buried about a foot in the ground, ACROSS/PERPENDICULAR to the direction of the sag. This greatly increases the surface area the post has to pull through to sag.
b. Again, if only concerned about sagging when closed, install a fixed rigid pipe from the hinge post to the latch post, underground. This gives you twice as much resistance to the post moving as just the one post.
c. Make a "bow" over the top, to tie the top of the hinge post to the top of the latch post... again, only helps when closed really.... and this won't be as effective as one buried underground, as the forces are transferred at the top of the post where it will have more leverage to move it than if it were buried in the ground. Burying that force transfer beam will also result in "resistance" on the sides of that buried transfer beam through the ground as well.
d. If your concerned about it sagging when swinging open too, you could make a "spoked wheel", and slip that over the hinge post after DRIVING it in.... and bury that in the ground about a foot.... this greatly expands the surface area and amount of soil that the post has to move through because of the leverage the gate is putting on it.
e. Install three posts on each end in a "V" shape, and tie the top of the hinge post to the soil level of the two anchor posts. This will help both when closed and when open...
Using a larger diameter post of course helps some too.... but it won't result in nearly as much "resistance" to the leverage placed on it from the gate as will these other solutions. You'll gain much more resistance through these methods. Obviously ALWAYS use a post heavy enough though so it won't be able to bend from the weight of the gate itself.
Making it into a "bow gate", with a "tie beam" across over the top, will maintain both posts in alignment, so your latch will always be lined up properly... but putting a "brace beam" between them buried in the ground will add more strength against the "sagging forces"... doing BOTH will make it a very solid installation. A properly installed "under the surface brace beam", that's literally fixed "permanently" to the posts on each end, like with a strap around the post and onto the brace beam, will also help considerably with these "sagging forces" when the gate is opened..... One could use a variation of this by putting a brace beam out to the opening direction as well, to another post buried in the ground.
A "wagon wheel" slipped over and fastened to/placed up against each post and buried, along with a"bow" over the top in the closed position, might be the simplest way to accomplish a really good, solid installation. Sometimes the "bow" can be limiting for clearance.
And for sure, if the latch doesn't automatically provide it, be sure to have a "rest" for the gate to be placed on in the closed postion.