Summoner Lvl30 starting quest

[Enkidoh]

Welcome to Eorzea!

Firstly, when you say you have done "everything you can do in the main scenario", have you completed the level 20 main scenario quest 'Sylph Management'? This is a requirement for unlocking Jobs (you can check your Journal under "completed quests" for it). The other requirement to unlock Jobs is you have to have completed all the quests given by your class's Guild including the level 30 one.

I had to refresh my memory about where the SMN Job quest is gained specifically (as I unlocked it back in 2013), and according to this page Thubyrgeim the acting ACN Guildmistress is the questgiver for SMN, so if you have satisfied the requirements and yet nothing is showing up, all I can suggest is try zoning out of Limsa and then logging out, and logging back in again, and trying again, as sometimes quest progression "sticks" and doesn't update the availability when you accomplish the requirements for it. For some reason zoning/logging out sometimes fixes this.

Other than that, I have no idea I'm sorry to say, other than, are you switched to another class while trying to get the quest? You have to be as ACN to get the SMN Job quest (this is the case for all Jobs-from-classes quests - classless Job quests have no such requirement other than level/story progression). So if this is the case, just switch back to ACN and try speaking to Thubyrgeim again.

EDIT: and checking your character's profile on the Lodestone it seems you only have ACN and are currently set as it (on the Lodestone profile anyway), but I notice you have the three gathering classes FSH, BTN and MNR unlocked and are around level 20ish each. Did you happened to have been set as one of those when you were trying to get the Job quest? (Crafting and gathering classes like FSH are considered just the same as battle/mage classes, so you have to switch class to ACN to get the quest to show up.

EDIT 2: and, it just occurred to me - does Thubyrgeim have a red 'quest locked' icon above her head, or is there literealy nothing above her head and she just talks to you like a regular NPC? If it's the former, try clicking on the icon as it will tell you why the quest is currently locked. If she has nothing above her head despite having satisfied the requirements, this may sound a silly question, but, by any chance have you actually already gained the quest/completed it and just forgotten about it? (This actually happens very frequently, especially players who take a break from the game and come back and forget what they have already done and ask for help trying to get a quest they actually have already active or completed, and after checking their journal they soon find they have it already).

Try checking your journal and if you have already started it the quest should show up in the active quests list. If it's completed a giveaway is the SMN crystal will be in the Soul Crystal section of your inventory waiting to be equipped (as well as being listed under Completed quests in the Journal).

Either way, good luck!