Does trample ability have any effect during a fight between two creatures out of combat?

I'll explain better.
When any card or effect allows two creatures to fight each other - for example, when a Territorial Allosaurus is summoned by paying its kicker cost - it is good to clarify how the various creatures' abilities still have an effect.

The question is this:
-"Does trample ability have any effect during or after a fight between two creatures out of combat?".
I give an example.
If two creatures are invited to fight each other, let's say a War Mammoth and a Scryb Sprites, after the fight ended normally with the Mammoth's victory, the fact that there are two points left that the Mammoth could deal with the trample ability, does it have any relevance in a case like this?
That is,following the same example: does the Mammoth's controller have the chance of dealing them to the opponent?

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    Wait, are you really stating, that first strike is taken into account when two creatures fight? Have you even read up on the ruling on fight?! – Erik Feb 18 at 10:09
  • Oh! Really? This puzzles me ... I was absolutely sure that the first strike ability applied to the fight ...! So I' m going to correct the question right now, at least on this point. Thank you,Erik. – ManoFromBerlin Feb 18 at 10:18
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    Have you read the accepted answer to the linked question? I guess not... – Erik Feb 18 at 10:25
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    Yes, it is true, now I have read the answer, and ... yes, they are the same! My question is covered in the answer to that question .... thanks Erik and Hackworth. And sorry! – ManoFromBerlin Feb 18 at 10:27
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    @ManoFromBerlin You could always try the search function. If you just type "fight trample" into the search bar, the question would have appeared as the 2nd result. If you get too many non-Magic-related results, you can narrow the search to questions with a certain tag, like so: "[magic-the-gathering] fight trample". – Hackworth Feb 18 at 12:19