I don't think I've ever seen the English dub of Godzilla vs Mothra: Battle for Earth, (1992), so I don't know if it's as bad as the critics say. If you watch this, at the 4-6 second mark, you'll get a taste of Indiana--Nihon style!
The Secret Vortex has this to say about the film:
"The only drawback to this film is the Indiana Jones homage at the beginning, where a young archaeologist (our film's nominal hero, although he doesn't do much but stand around and watch like everybody else in the film) runs through several variations of famous Indiana Jones scenes before the main plot begins. I guess they thought it would a unique way of starting a Godzilla film, but unfortunately they don't even bother to parody Indiana Jones, which might have worked, but instead play it straight, so that if feels less like a homage and more like a ripoff."
I wouldn't be quite that harsh. Let's take a look at the ゴジラvsモスラ pamphlet and see if we can find any references to Indiana Jones (interupted by a few versions of the Mosura song by the Cosmos!)
There is relatively little there to go on. So let's check out the mini-Encyclopedia.
Still not so much, then perhaps if we check out the Manga version?