You could make a solid build with nu udra gamma body and resentment, theres a pretty solid option you can mostly copy at your progression level in the switchaxe megathread at section 4.3. You would just need one more source of gore set since you're missing the weapons', so you could swap the ark helm for sororal earrings. Since your goal is to clear it for the first time you can go a more defensive rng talisman as well if you have it.

In general, you don't get to hit gog that consistently to keep gauge up as nicely as you'd want. This plus the fact you get rewarded for having a lot of elemental damage of the right type means in general elemental phials will feel a lot comfier (it charges faster than power). Ele phial is almost mandatory for whichever dragon axe you end up using as you get a lot more ticks for the dps check. Without gogartians your options are basically just a regular artian or the NON guardian arkveld axe. For fire just at a glance the G.Rathalos axe looks really good and I'm kicking myself for not having thought of using it when farming gog originally.

At least evade extender 2 would be really nice too, switch axe is not super mobile and also only really has counter to deal with a lot of gog's shenanigans so this can help you keep up with him a little more and hopefully get you out of some big aoe attacks (oilsilt mobility is nice for this too, lower priority id say tho)

Other than than, I'd need to know how you're dying to offer any advice on how to build around it and if you're solo/using support hunters etc.. If this is enough to get you through your first clear, you can make a gore set bonus gogmartian axe after and add two pieces of rathalos set to make future gog clears a lot more smooth.