Can I get a Covid extension for my tourist visa without using the 30-day extension first?

If "you're here" happened to be Phuket, you would be required to use the 30 day extension first.

I came to Thailand on a 60-day tourist visa in December. Since I stayed in Bangkok most of that time, I went to Chaengwattana in February to get an extension. At that time, the rule was to extend the 30 days first before I would be eligible to apply for a Covid extension. I have seen no subsequent evidence from Chaengwattana suggesting this rule has changed. As others have said, your mileage may vary depending on which immigration office applies to you.

Another essential point to remember for your Covid extension (if/when that time rolls around) is that immigration officers typically ask for a TM30 receipt before accepting your application. The TM30 receipt must show an address within the jurisdiction of the immigration office, meaning if your TM30 says you are staying somewhere in Bangkok, you must apply at Chaengwattana. Similarly, if your latest TM30 is for Koh Samui, you must apply at the immigration office there.

In my experience, and from what I've heard elsewhere online, a TM30 print-out/receipt is not strictly necessary to extend your tourist visa. But, seeing that TM30 reporting is a legal requirement, I would generally advise getting one before engaging in any interaction with immigration.

That you want a covid extension doesn't mean it'll be granted because they're at the discretion of the issuing office/officer.

AND

The general rule is you must take the regular 30 day extension allowed before you apply for a covid extension.

So what I'm saying is, I see a visit to your local immigration office to ask them IF you can apply for the covid extension without having taken the 30 day extension first.

There are over 70 immigration offices in the country and they don't all follow the same rules. That's the only way you're really going to know.