Can I apply for a 30-day visa extension immediately after arriving in Thailand with a 60-day tourist e-visa?

You skipped the most important information, which immigration office?

You need to wait for a specific time to apply for 30 days tourism extension. But it does depend on the immigration office how long you need to wait. Some offices including Bangkok and Chiang Mai allow you to apply when you have 45 days or less with your current stamp, this is the earliest nationwide. Most offices accept your application when you have 30 days or less. A few would tell you to come back within the last couple of weeks left. and a few including Jomtien wouldn't accept your application until you are in the last week of your stay.

So it is the key information which office of nearly 80 you are going to use. Aka the office that serves the address in your TM30 receipt. You need to check your local office.

This is the general information for 30 days tourism extension.