Where did you get the term GRS? I haven’t seen that anywhere in Fiverr’s help materials or elsewhere so if it’s something new it would be useful to know. In the past, Fiverr has not made any promises or guarantees regarding anything to do with gig “ranking” or search positions. In fact, many gigs are not ever listed in search at all.
So far, if a gig is brand new and it doesn’t set off any instant red flags, it will probably be listed in search after it gets indexed. That can take a few days to a week or so. Sometimes something happens during or after the indexing time and Fiverr realizes the gig is not something they want to promote. They call that their editorial focus. If they decide the gig does not fit their editorial focus but it doesn’t not break the Terms of Service, they don’t automatically take the gig down, but they don’t promote it for you. In that case you can promote it yourself if you wish, or you can switch for a gig that is in their editorial focus.
Gigs that do end up in search are loosely positioned on a rotational system and by algorithms that Fiverr doesn’t share publicly. In general things like sales, good reviews, traffic, good related keywords, and uniqueness may push a gig higher. You can’t rely on that in any consistent way, though. I’ve seen gigs even in the recommended column that are fairly new and have some 1 star reviews on them. So, if there is an actual “GRS” or “Gig Ranking System” I’ve never heard of it.