it is basic , we have lesson from history , you need to look Normandy invasion

to invade another continent which enemy is very experienced and waiting for you , you need superior power at sea and air
aircraft carriers , battleships , tac bombers , attack bombers and other similar things , your ground units are useless for first stage , send some submarines to enemy continent and collect information about coasts , find a weak point to landing and bomb around it with planes and ships , and dont forget while disembarking keep your ground unit convoys with your ships like cruisers battleships and protect them against enemy air and artillery attacks , after capture a weak point with ground units along coast with support of your ships and planes

if you are talking about very very late game , and if you have nuclear rockets find a close island to big continent , place rockets to there , and try to collect some information with spies about enemy army locations , when you see them send rockets

Land in a remote area.

For example, say you're invading South America. Keep out of sight, and land in Tierra del Fuego. The opponent is not going to keep a significant force there, unless they know your plans. They probably won't even have air bases to cover that area. Even if they do, your cruisers (most important naval unit in CoW) protect transports while they disembark, and AA guns protect the army after they land. As long as you're far away from enemy artillery and surface ships, they can't stop you. After that, you build an airfield, and you're in business.

as he said above if we talk about south america around of Tierra del Fuego's windth is small , very hard location to defend with railroad guns artilleries and other ground units because you can bomb them with ships easier and probably enemies will be tend to hold units at the middle of the continent

The point is to establish yourself on the new continent before the counter-attack arrives.

Occupy favorable terrain, like hills, to give your artillery + AA units an advantage. Build forts, if you expect close combat. Build multiple airfields, so you can start to scout the land around you, see what's coming, and establish air superiority.

Once your army is in place, your navy can go on the offensive, ambushing and sinking the enemy's navy, harassing land units that travel along the coast.

This is also the time when the opponent tends to make a mistake. They rush to meet your invasio force before it gets too far into "their" territory. They might send unprotected artillery your bombers can kill, or refuel airplanes in range of your warships.

The point is, you're not fighting a well prepared opponent from a vulnerable position. Your army and air force are set up on land, and your navy is free to roam. They don't have to shield disembarking transports from air attack.