On the first game today in exactly half an hour and on the second
An hour is a relatively long period of time, even in this game. Generally speaking, an opponent that's been given that long to build up could have anything. This is
not a rush by any means, and a large conventional fleet by this point is
typical. You need to speed this up a bit more; I typically am capturing planets at a rate of one every 3 minutes in the early-game, which means I usually have around 6 planets within the first 15 minutes. You don't need to move that fast to beat the normal AI, but it should give you an idea of the kinds of speeds that are possible.
The two games I played were 1v1, no pirates, tec with the enemy player on either hard or easy economy
Hard has a small resource cheat, easy has a small resource penalty. Losing to hard is no big deal when you're beginning, but losing to easy indicates that you have a fundamental issue with your approach, and need to look at your speed and spending priorities.
I expanded quickly onto a volcanic planet and two asteroids, all fully upgraded.
You only need to buy the civilian population upgrades (and for ice/terran/desert planets, you only need two of them). The other upgrades are "nice to have" but usually unnecessary, and buying them all is exorbitantly expensive.
This on its own would bankrupt you and cripple your early expansion.
At this point I was invaded by the enemy player from nowhere ( once on a map with no jump lines and once on a map with jump lines but no sign of them being used by the enemy player)
You cannot "see" enemies on phase lanes without the appropriate research, and even then the warning you get is so short that the research isn't worth your time. You need proactive intelligence so you see the incoming enemy fleet before they arrive. I assure you they are
not coming out of nowhere, and you can even watch the replay and see the enemy build up and attack.
No enemy player ship (Class Marauders, Class Evac., Karrastra, Skirmishers) was even destroyed and was five planets away from my Capital Planet originally.
Without knowing the number of units involved, I can't comment much, but from the sounds of things you were outnumbered significantly by heavy units.
I poured Javelises and Cobalts into the battle
Given the units you've described, massed Javelis would be your best response. Skirmishers and capital ships in particular are no match for a large bulk of Javelis. The AI didn't have Enforcers, Carriers, or Sentinels, so there's really no reason to use anything else. A steady trickle of units won't do much, though. You need to step back and regroup into a larger force, sacrificing planets if need be. Preferably you'd want those units
before he arrives.
How do you account for the time spent on this game doubling each time it is played, and terminating at exactly the right time?
The "on the dot" factor is probably a fluke. I can tell you from experience that timing is
NOT a forte of the AI. When I do my speedruns (typically my opening attack is 10-20 minutes into the game) I have the AI down for the count long before the one-hour mark, and I prey on the AI's terrible timing to throw off its defenses and pin it down before it can establish itself.
As for replays, this is your path:
C:\Users\<UserName>\AppData\Local\Ironclad Games\Sins of a Solar Empire\Record-Singleplayer
AppData is a hidden folder; you'll need to reveal it from folder options.
I've got an old replay I uploaded for someone else with similar issues as you: http://www.filefront.com/15978297/Comp%20Stomp%2003-30-10.record
This is unfair difficulty completely and utterly beaten in 70 minutes. You'll notice that the serious fighting started around the 30-minute mark, and from that point onwards I was hitting hard on two fronts while bolstering my economic, tech, and fleet composition. Towards the end I accidentally built too many Iconus Guardians; didn't have enough firepower and the final battle dragged on a little long as a result.