Just here to give away my leftovers. How do I move up from the kids table?

You need to do more giveaways, So it will be increased the slot.

You can write to the mods and explain to them that you wanna get over it quickly. It's an anti spam measure mostly. They should let you make them

There're two ways, both unreliable, for one reason or another.

The first, and most obvious one, is to just ask support for more slots. Pretty straightforward.
The negatives are that 1) it's unlikely to be answered in a timely manner, if at all, being a low priority ticket, and 2) you're unlikely to get a positive answer, being a new user with no track record.

The second is to just spam short giveaways, you get an extra slot every 3 successful ones, in addition to getting back those you had spent. Starts slow, but quickly snowballs.
It's unreliable because, especially at low levels, your winners are likely to be 24/7 online bots whose owners only come around once per week to collect weekly loot.
Invite-only giveawasy are a bit more reliable, as you reach actually active users that way, rather than those who consider this a "gleam v2.0".

But there is nothing better than having the vision of a child. Grow up but keep that in mind.
As mentioned above, contacting support is the only alternative to being patient.

The others' answers are based on the premise that you want to raise your contributor level, but you made no direct mention of that.

If you goal is just to unload keys, you can use the Orphan Keys thread. Doing that would mean you get no credit toward your contributor level.

As others answered, as soon as people mark this first GA as received, you will get more slots. I mean, we don't want you to be generous all at once, do we? :D :D

Anyway, as a long time user, let me say "welcome to SteamGifts", hopefully you will enjoy your stay. The only essential advice I can give is: no matter what people tell you, no matter how they say it, never never EVER

Yes, my jokes aren't that good.

View attached image.

You can either make giveaways with the button in top left, or find people in discussion threads to share them with, or just drop the keys for the bots to hoover up, in one of the several key drop threads....

I prefer "anti-ninja" key drop thread....
https://www.steamgifts.com/discussion/tnWVh/anti-ninjas-key-drops-no-keys-in-messages-though/search?page=999

and "Don't like bots.. so invite only..."... links have a few extra characters that need to be deleted, to keep bots from auto-entering....
https://www.steamgifts.com/discussion/Rl7Jo/dont-like-bots-post-your-random-invite-only-giveaways-here/search?page=999

Just write one-hour giveaways. It will be three at first, then it will quickly grow

Give them to me and I'll do it for you, 100% free and legit