In R/B/Y (and remakes)you can catch all the legendary Birds before the elite 4 , (Also Mew Glitch is very easy to perform)
G/S/C has the legendary Beast roaming the overworld (remakes suicune is post game)
R/S/E Have the Regi's (Brail quest),
Emerald has Mew and Deoxys event tickets.
D/p/PL you can catch the Lake Trio, (remakes give you mew and jirachi for owning Lets go and Sw/Sh)
B/W have tornados/thunderous(roaming) swords of justice, and Victini via Liberty pass.
B2/W2 don't have the Genies but you can get them all with dream Radar if you have that. Sword of Justice again
X/Y None
ORAS Like the original you can get the Regis but now you can also get a Latios/Latias with other being accessible if you get the Eon Ticket. After beating the box art legendary and getting Nat Dex you can access the portals to catch the legendary Beasts (after catching Ho-Oh/Lugia), the lake trio, heatran, cresselia, the SOJ, and the Forces of Nature once requirements are met.
Sun/moon none
Ultra S/M ultra wormholes allow you catch like 20 different legendaries before elite 4 but is late game during the ultra necrozma story stuff.
Sw/Sh only eternatus can be caught before the endgame (base game). DAs are possible in DLC before 1st gym but are high level. Regis and Galarian birds once you have 8 badges. But realistically Kubfu will be the one you get and once its in the mid 30s you can return to the isle of armor to challenge one of the towers to evolve it. The swords of Justice and Calyrex cannot be caught until after the post game.
Sc/vi Wo-Chien, Chien-Pao, Ting-Lu, and Chi-Yu can be caught before elite 4 but are level 65 and will disobedient until you get all the badges. DLC for teal mask can be completed early and the legendary Pokemon can be caught but they are hard coded to be at like level 70 except for ogerpon which is Level 20 which makes it the only one that'll obey you before getting all the badges
Edit: added info later generations and fixed errors addressed in comments.