This might help clarify what I mean by "affect"
2 hypothetical Golfers both average 5 strokes per hole (90 for 18). Per 18 holes, both average two 3s (11.1%), four 4s (22.2%), six 5s (33.3%), four 6s (22.2%) and two 7s (11.1%). Pretend these 18 scores are like a deck of cards (and ignore par/difficulty of hole differences)
Golfer 1's scores are INDEPENDENT of each other meaning he shuffles his deck after each hole. If he makes a 3 on the 1st hole, he still has a 11.1% of making a 3 on #2. You would expect him to average 88 after opening with a 3 and 92 after opening with a 7 as you would expect him to play the last 17 in 85 strokes regardless of what he makes on #1. A score he makes on one hole has NO EFFECT (or predictive value) on the score on any other hole.
Golfer 2 does not reshuffle his deck after each hole. His scores are DEPENDENT on what he has made on previous holes. He will average 90 regardless of what he makes on the opening hole. You can predict what he will make on #18 with 100% confidence based on what he scored on the first 17 holes. If he makes a 3 on #1, he will take 87 on the remaining 17 holes, but will only take 83 on the last 17 when he starts with a 7. The score he makes on #1 affects the rest of the round.
So how does "reversion to the mean" work with Golfer 1 who plays each hole INDEPENDENTLY? If he opens with anything other than a 5, we expect his average score for the round to move towards his mean score of 5 BUT THIS DOESN'T MEAN THAT WE EXPECT IT TO GET THERE BY THE END OF THE 18TH HOLE. i.e. Suppose he opens with a 3. We expect him to average 5 on the remaining 17 holes for an 18 average of 4.89 for the entire round. If he ends up shooting 88 as expected, his average score started at 3 (after the 1st hole) but moved towards his expected mean during the rest of the round.
My point- If your average 18 hole score is the same regardless of whether you start with a birdie or a triple bogey, then you are showing characteristics of Golfer 2 where the score you make on hole #1 has an effect on what you score the last 17. Phil's and several other posts seem to think Golfer 2's scores are independent, but drawing from a closed set that is not reset after each draw means future results are effected by past results.
(FWIW, I also believe some golfers may start drawing from a new deck with a different composition of scores but wanted to keep the above examples as simple as possible)
If someone averages 90 that doesn't mean they shoot 18 over every round. So the variables would be a lot more than you are saying here. Also an average in golf is in constant flux especially if you are using the handicap system. Any round can be below or above the average and the first hole only truly affects it as part of the overall score of that round. Other than mentally of course which is what I am sure most people thought you were going with this originally.