It has happened around the world though. Early American settlers from Britain often had large families, and therfore population growth driving the expansion of American settlements.
https://en.wikipedia.org/wiki/Demographic_history_of_the_United_States#Historical_population
Having the relative support of a leading state and economy somehow differs from scattered settlements dominated by another people.
What about a active religious tradition?
That's not really the point, again : it's probable that IOTL they had a distinct religious practice, but being scattered in small settlements in a relatively desolated region does.
How did the Hungarians manage to pull this off?
Managing to mobilise enough wealth trough raids (a mobilisation that eventually reinforced the chiefdom structure) , moving from pastoral to agricultural subsistance successfully when raids declined, structural Christianisationand being the last wave of large settlement (which is related to the reinforcement of Eastern European states, with Poland, Rus', etc and the regrowth of Byzantium's power)
Hoe did the Vlachs pull this off?
How did the Albanians pull this off?
We discussed this in another threads, IIRC : eventually, it was the capacity of both to form relatively isolated communities in highlands, relatively far from the political/economic centers (as it happened for Pannonian Slavs, eventually) then survived among other reasons thanks to regional stabilisation (Hungary, Byzantium, etc. which helped transhumance and self-subsistance).
Then it's a matter, IMO, of historical contingence : some peoples were able to form broader entities and expand culturally trough "state sponsoring" (such as Albanians in New Epirus and beyond; or
Vlachs in Thessalia), filling a political void as Transdanubian Vallachia. Some other communities simply disappeared, and some other (most of Aromanian communities for instance) didn't outright disappeared before the XXth but never managed to form strong enough political identities.
Gepids being settled in the Pannonian basin, which was basically an highway, and in relatively few numbers on the other hand...Again, there's a reason why peoples in this place were essentially never heard of after a while would they be Romans, Germanic, Avars, etc.
Perhaps they could settle inside the Ostro-Gothic kingdom?
That's possible, even if I don't see the reason for this settlement myself : Ostrogoths were fine enough with the permanence of Gepids in Pannonia, would it be only as buffer march, and Gepids seemed concious enough of their relative weakness not to try attempting funny like invading Italy.
Now we could consider something along a large numbers of Gepids settling in Italy, regardless of the reasons (I mean, there's probably a reason we could find that would be both plausible and workable enough), but that would mean at short or middle term cultural and identity integration among Goths, and extremely likely the loss of a Gepid identity and of course language : Gaul Saxons and Burgundians were eventually "Frankishified" (meaning Romanized), Suevi were 'Gothicized" (meaning Romanized), etc. (you know where I'm going with) and we're talking of people with a significant presence : some thousands of Gepids have no chance to escape this in Italy of all places.
Heck, it might have actually happened, with Gepid settlement being mentioned by Paul the Deacon in Lombardic Italy.
If not perhaps some mountains in Transylvania could provide a safe haven or safer haven?
It's likely that's what part of them did IOTL, there's some tombs and necropolis in Transylvania that were attributed to Gepids. That some of these were apparently profaned and robbed recently after burials could be interpreted variously, but IMO highlights a certain pauperty of everyday-life, especially giving the militarized way-of-life of Gepids : either they maintained their way-of-life and integrated with whoever "was at the top of the foodchain" (which is probably what many Pannonian Gepids did), or they accepted to decline into pesant communities (which was a choice neither Vlachs or Albanians really had to do).
This could be a scenario where Gepids are not under direct Ostro-Gothic or Roman rule.
I agree that this kind of scenario is perfectly workable (and probably the most plausible) but for their survival they need a reinforced presence of whoever rules in Italy and Byzantium, for stability sake, which is politically and strategically not that easy to balance with Gepids' "interests".I tried to work this this above.
EDIT : Arguably, you could have a Gepid survivance, the same way you had Thuringian survivance and Bavarian build-up in Central Europe without necessity of a "both-banks" approach, but at the latest you need to deal with Avars, and have a strong change of strategical priorities in Constantinople either allowing the survival of Gothic italy and its overlordship on Gepids; at least giving up on Illyricum (which was a strategic focus of ERE).
Re-EDIT : Maybe even having somehow the permanence of a Patrician Italy, while ERE is too busy on its eastern borders?