Although the two words have very similar meanings, these are problems with collocations. (Common patterns of native speaker usage.)
For the first sentence 'to turn down an opportunity' is the stronger collocation here. (Usually you say 'to miss a chance'.)
For the second sentence 'at the earliest opportunity' is the collocation.
For a good self-study book to improve your awareness and use of collocations, try 'Check Your Vocabulary for Natural English Collocations' by Alison Wooder and Jon Marks.
Amazon.co.uk: Check Your Vocabulary for Natural English Collocations: All You Need to Improve Your Vocabulary (Check Your Vocabulary): Books: Jon Marks,Alison Wooder
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