I am well aware that on my Physics Stack Exchange account, I have asked a few good questions and also some bad ones in the past. For the Curious badge, I have an 8/5, but am unable to get it as I do not have a positive question record. I am unable to delete those questions as others have already spent time investing an answer. Hence, I would like to ask, given these circumstances, is there NO way that I can even get these badges?
One non-well received question in the past
does not a summer make does not disqualify you for these badges forever. In fact, most people (including me) have those. They just have the consequence that you need to make some additional well received questions, beyond the usual 5 for Curious.
Note that even if you would be able to delete a closed/downvoted question, it will still count as a non-well received question; in fact, it carries a higher penalty than just a closed/downvoted question:
A positive question record means you don't have too many closed, downvoted or deleted questions, overall. The formula is
(TotalQuestions - Negative - Closed - Deleted) / TotalQuestions ≥ 0.5. Questions that qualify as Negative and Closed and Deleted count three times in this calculation!
(from the FAQ)