Only the original author of the question can accept an answer.
If they decide not to accept an answer, that's OK.
We prefer people to accept an answer, but we can't enforce it, or select an answer for them. Besides which, I have personally had old answers 'accepted' years after I wrote them.
If the user is truly new to Stack Exchange as a whole, it can be useful to leave a temporary comment encouraging them to accept an answer (perhaps linking to the help centre as below).
Accepting an answer doesn't close the question; new answers can still be added at any time. (The new answer might even be 'better' in the eyes of the question author; this is why the answer marked as accepted can be changed).
Given a clear question with good answers, the site is already winning. The lack of a green tick on one of them does not mean all that much.
The votes from the wider community are a usually a better guide to answer quality than the green tick anyway.
What does it mean when an answer is "accepted"? (help centre)
How to deal with abandoned questions?
Would it be possible to have a “community accepted” feature?