Buy TF2 item without buying Steam games first

I started playing Team Fortress 2 and ran into the item limit which is a really bad thing because now I can't switch teams during the game when I'm asked whether I volunteer for switching because if I accept, an overlay which can't be closed, is opened. Discarding items doesn't really help. I tried this after experiencing what's described below but if you find new items during the game you're playing, you're shown the overlay, too. Discarding items then, doesn't allow you to dismiss the overlay.

I went to buy some random item from the store but wasn't able to because this message popped up in Steam:

Do I really have to buy some game on Steam and then wait 30 days, just to buy an item in TF2 to get rid of the low item limit and its side effects? Is there a way around this?

I know very little about Steam and created my account for the sole purpose of playing TF2. Sorry if the solution is obvious and I just can't see or find it.

In case it's important: I live in Europe.

Unfortunately, there's a restriction on the Steam Community Market to prevent fraud or scams from occurring. So yes, you'll have to make a purchase on your Steam account worth $5 USD (regardless of where you live) or more in order to use the Market. From their Community Market FAQ:

Your account must have a successful purchase older than 30 days, but not older than a year in order to access the Community Market. The purchase of wallet funds, games, DLCs and software meet this requirement. Retail CD key activations and gift purchases do not satisfy this requirement.

In regards to where you live and its effect on currency to this extent, this is elaborated on in the Limited User Accounts FAQ:

What if my Steam store currency isn't in USD?

If the Steam store isn't in USD, we will track the purchase amount in USD by converting each purchase total made on Steam using daily exchange rates. Once you have made the equivalent of $5.00 USD or more in total Steam purchases, you will gain access to the restricted Steam features.

Thus, if you don't want to buy something for the sake of accessing the Market, you could just put $5.00 USD worth of currency into your account's wallet (as this qualifies as a purchase for your account), wait for the purchase to be 30 days old, then use it in the Market, once you have access.

This is a complementary answer to Vemonus's answer.

There are items which expand your backpack. I noticed that I had items which can be unpacked in my backpack and unpacked one. It contained 8 items, one of which was able to increase my backpack's volume by 100 items. Would've been a lot better to have figured this out before deleting items to make space several times.