If I can make a suggestion, consider going to the Advanced settings, and dropping the number of players by 30-50%. If you drop by 30%, all but one or two will start with you on the homeland. Drop by 50% and all will. Then the Exploration Age becomes are real land rush and a great deal more fun. And more historically accurate as well.
I my experience, on a Standard-sized map, the first 5 Civs including the Human player) go on the Homeland Continent(s), the last 3 in Distant Lands. I started removing all three Distant Lands Civs, but that had some bad effects:
1. It made the whole Exploration Age a Yawn - much, much too easy and positively boring to play.
2. It also reduces competition from other Civs for Wonders in Antiquity and Relics in Modern, among other things, so overall I estimate it was the equivalent of dropping down an entire order of Difficulty.
After some experimentation, I've been playing with 7 Civs total in Standard maps, which means only 2 in Distant Lands. That still provides fairly adequate competition, but doesn't completely fill Distant Lands with AI settlements before Exploration Age even starts. You are still at the mercy of the map in getting to the 'empty' part of the Distant Lands first and finding any Treasure Resources, but it's less of a complete impossibility without going to war by Turn 15 of Exploration Age just to claw a foothold onto the other continent.
The game and the players are missing a whole raft of possible decisions in the game and game set-up that would go a long way towards solving, or at least ameliorating, these kinds of problems:
1. Allow us to specify Distant Lands configurations separately from Homeland, Not only in overall terrain configuration (continents, archipelago, fractal, etc) but also in biome (wet, hot, dry, cold, mixed) and especially in numbers and types of Opposition: number of AI Civs, numbers and types of IPs - including the possibility of having Distant Lands entirely full of 12 - 15 IPs, all Hostile, which would give the Conquistadores a real run for their money.
2. Right now, and related, IPs can only become City States if they are subordinate to a Civ - there are no independent City States in the game as there were in Civ VI, and therefore all interactions with IPs are either fighting them as Hostile settlements or as part of an AI Civ, or throwing Influence at them to subordinate them. Include a mechanism for IPs to 'evolve/grow' into Independent City States with possible permanent (ie: from Age to Age) status, and the number and amount of diplomatic and other interactions with them could multiply dramatically: among other things, a Distant Lands entirely filled with IPs could be exploited with Diplomacy as well as or instead of Domination and the overall number of meaningful decisions for the gamer would increase in a game that has far too few of those at the moment.
3. The latest patch started (hesitantly) towards making Treasure Resources more flexible, but did not begin to go far enough. Make the type if Resources designated 'Treasure' dependent on in-game play. For example, Horses might become a Treasure resource depending on how many cavalry units are built in Antiquity compared to the number of available (Homeland) Horse resources. Gold and Silver should change status depending on a more-developed system of Coinage: adopt Silver coins (which should actually be the default standard) and Silver becomes a Treasure Resource instead of just decorative metal. Build a bunch of Carracks and Galleons, and Hardwood becomes a Treasure Resource wherever you can find it. Rarity of resource should count in-game: anything found on Distant Lands not found on Homeland terrain should be, by definition, a Treasure Resource.
This alone would make the entire Treasure Resource/Fleet system more flexible and dynamic, leading to an on-going search for real and potential Treasures all over the map and competition to settle, conquer, or otherwise sequester resources you need or anticipate needing.