A few solutions if rushing is so disturbing you'd rather not play AOE3...
/rant on
1. Play single player. On easy.
2. Play a different game (might I simply suggest AOE2, which still has a large player-base?). There are lots of them out there. RON, for instance, offers a no attack timer option in its game settings. There's nothing wrong with buying a game you actually want to play against other people in if the game you currently own doesn't fit the bill. No game is designed to be "for everyone". Even attempting that would be absurd.
If you didn't know, go read the Dev blogs and you'll quickly discover that AOE3 was designed to be different from AOE2 in at least one very important regard: Combat is INTENDED to take place very, very early in the game because the vast majority of gamers (according to ES market reasearch) found the first 8-10 minutes of each AOE2 game to be sluggish and boring.
3. Make a lobby game with the title "no rush for X minutes". Put anyone who violates your little rule on your "pest" list, anyone who complies on your "friends" list, and in short order you'll have quite the merry circle of friends who all like to play the slow game. It achieves everything a "no rush" option does, without having to wait for a patch.
4. Stick to playing against people of your own skill level. Use the ladder that Elpea and his associates have so kindly provided. And bear in mind that 1600 isn't the "zero level" or "starting level" or anything like that. It's the "average gamer" (by which I mean the player who is roughly on the mean). If you can't do anything against the rush to make the game last longer than 20 minutes, you're probably not an "average gamer". But that's okay... 49% of gamers aren't! And they're all looking for people to play against competitively, as well! You might actually like playing against people of a comparable skill level, if you sought them out, instead of making this laughable effort to suggest that you really would be at least a "rook" or "intermediate". except for that pesky, unfair rush thing.
Hell, I'd be a chess grandmaster if not for that stupid, unfair bishop piece. I mean, unlimited diagonal movement? Come on!
5. @ Moshelevi... I begin to understand why people are so often annoyed at you.
"At some point I get to have 90 villagers and unlimited supply of resources."
No kidding? If I get up to around 90 villagers, fully upgraded, I have access to virtually unlimited resources? Do you suppose this is why EVERY OPPONENT I EVER PLAY AGAINST targets my villagers?
"When I get to that stage I can take on almost every player, as I keep a constant flow of units from numerous barracks/stables and maintain the population at 200 all the time."
No kidding? You mean when someone is a bad enough player to allow you to reach this stage, you're always able to defeat them? The mere fact that they were unable to mount an attack on you for 20+ minutes wasn't an indication that maybe they didn't know what the hell they were doing?
"So Cerses629, you are going to win easily against me if you can rush after 6 min.
But if you give me 17 min of “cease fire” (I can get to industrial around 14 min with 45-50 villagers), I promise to deliver you a challenging game."
No Kidding? Oh wait, you won't. A big army might walk over a noob at the 17 minute mark, but I promise you that Ceres will have a bigger army with better upgrades due to more efficient use of villagers, and will micromanage it to the point of slaughtering your troops while taking minimal casualties.
"My point here is that once you allow your opponent (even if he is weaker than you) to have a large army and good economy, the game will be more challenging and it won’t be as easy to win it (unless you are playing against a very weak player)."
No kidding? Or your story could just prove that your army management skill is... weak. Your opponents were better at it, even thought they were worse at economy.
So point 5 is this - if you want to ignore the economic side of the game and clash with big armies, just play deathmatch. All the best troops, all the best upgrades, vast stockpiles of resources, no need to wait to get access to them. You can throw endless troops at your opponent all afternoon in deathmatch... If you can manage them as well as you claim.
Oh wait, that's too fast, too - they attack before you're ready. Well, there's always turn-based games.
/rant off