Look, in a level based system, some things require you to be a certain level before you do them.
It's pretty hard to be a first level weapon master.
Sure, depending on what you mean by 'weapon master', but if you are playing your character to be a weapons master... then what?
If you want to start play as the finest swordsman in the world, you can do that. You just don't start at first level. You start off at above whatever level is normal for the setting. This is however true of the 'first level' of any game system, even one that don't have levels. By default GURPS starts you with 100 character points - probably about the equivalent of a 3rd or 4th level character - there are many things you won't be able to buy for that. MM defaults you to power rating 10. Every system tries to ensure that you will fit to the fundamental law of RPGs, "Thou shalt not be good at everything." Even something like Exalted where you are veritable demigods starts you out with a vast hierarchy of more powerful beings above you and with plenty of room for mechanical growth.
If you start off play as the finest swordsman in the world, then for the most part there really isn't much room for mechanical growth. You've already reached the ultimate. What particular story are you wanting to tell with that?
I mean, in terms of absolute power, it's sort of hard to be a 1st level god. But there is nothing really that stops you from doing that if that is what everyone wants to do. Perhaps your problem is that you just need to run one wildly Monte Haul over the top epic campaign to get it out of your system. Take all the brakes off, start at high level, and just go nuts with world breaking world spanning yahoo.
It's pretty hard to be head of a religious order at first level.
No it isn't. It would just be an unusual GM that would allow a PC to have that much influence. For one thing, it's a nightmare to adjudicate. I've been in campaigns with the players as rulers of various sorts, and as a player I was doing more work keeping track of my holdings, retainers, hirelings, and income than many GMs do to run their campaign. My 'character sheet' ran out over 100 pages. It was fun and it's definitely different and I have some awesome memories of that campaign, but I can't criticize any GM for not wanting to go there because my DM was putting the work of a full time job to run the game.
It's pretty hard to be king of a land at first level.
No it isn't. Presumably 'boy kings' who take the throne without much inexperience aren't even particularly rare. Such boy kings might also be at least the nominal head of religious orders - high priestly kings, uniting church and state. Again, it's just an unusual GM that would allow a PC to have that much influence. It's possible to start my campaign as the son or daughter of a king however, and I had one character in the campaign start with royal blood so they were literally in my game a 'Princess' and NPCs addressed her as, "Your highness". IF that is what you want, I'm fully willing to support it. If what you want is a administrative, political, military campaign, and everyone is in agreement, I'm fully willing to run that as well - but it certainly doesn't require you to be more than 1st level. Authority isn't solely the result of how many levels you got; some people, monarchs in particular, are born with it.
If I'm waiting three years to play the character I actually want to play then you can bet I'm getting frustrated.
I can honestly say I've never had to wait to play any character that I wanted to play. I'm not even fully sure I understand the complaint.