At this point, you would gather some evidence such as compression, fuel pressure etc. in ideal circumstances.
It could be as simple as resistance between the battery and the starter. Verify engine health and perform a voltage drop test between the starter and the battery for resistance. The voltage drop would clue you in right away to electrical related issues. However, the starter could be the culprit or perhaps a fuel filter is 'really' clogged and the fuel system must 'build' pressure for it to start? Perhaps injectors or something else relative to combustion mixture that may cause a startup delay of sorts. It could just need plugs, but that might be a stretch.
Also, if going to check compression may as well inspect the spark plugs for evidence that may clue you in to something else.
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