How can I check my resume for ATS problems without any tool?

You can do a reliable basic check with nothing but your PDF and a plain text editor. It takes a few minutes.

Steps:

• Open your PDF and select all text. If nothing highlights, it is an image and needs rebuilding.
• Copy and paste the text into a plain text editor such as Notepad.
• Read from the top: your name and contact details should come first.
• Check that each job title, employer and date stays together.
• Look for strange symbols where bullets, icons or special fonts were.
• Search for the key skills from the job advert and confirm they appear.

If something is missing or jumbled, simplify that part of the layout. This test does not imitate any specific employer's system, but it catches most of the problems that matter.