This might not be as much of a problem as you think. Why? Because munchkining, minmaxing, optimising, whatever you want to call it - is severely limited in 5e. The main techniques for it in previous editions of D&D involved things which are significantly less effective in 5e.
Multiclassing has been crippled by the all-important ability score increases/feats being a feature of class advancement instead of character advancement. There is currently a limited selection of classes and feats, so taking advantage of obscure classes, prestige classes, variants, and feats is no longer an option.
D&D 5e also introduces the concept of 'bounded accuracy'; see here for a good explanation of this idea. There is only so much it's possible to do to optimise a character in 5e, and the gap between an optimised character and an unoptimised one will be fairly small.
Your players will still spend time optimising their characters, of course, but that's not necessarily a bad thing. If a player hasn't spent any time on their character, that's a sign that they may not be particularly invested in them.
As far as creating playable characters with reasonable backstories goes, this is a great opportunity to use their munchkin-ness against them. They're going to want to choose a certain background for the proficiencies it offers - make them justify it. You want to be a Sailor who became an adventuring Wizard with a single level in Cleric? That's fine, but you'd better have a damn good explanation for it.
And using their munchkin-ness against them is a great technique to make them roleplay, too. When they create their characters, they'll choose a bond, a flaw, an ideal, and a trait. Let them know that you're happy to hand out inspiration (which is incredibly powerful - advantage to a roll of your choice? Sweet damn, who wouldn't want that?) if they play their character. Positive incentives have been used to motivate people to do what the motivator wants for years, because it works.
Quick bit of backup for all this - I'm DM-ing 5e for a group consisting of 3 munchkins and 2 roleplayers. One of the munchkins is so bad he walked into a core-only 3.5 game and insisted on creating an Artificer. And you know what? He's playing a single-classed Fighter, roleplaying as much or more than the roleplayers, and (as far as I can tell) having a great time doing it. (Oh, and he also has by far the most extensive backstory, he really got into it when he was choosing his background options.)
Best Answer
I play this character. My GM and I discussed the build extensively before starting Storm King's Thunder because I was worried about this. Both from pre-planning and from experience, here're the things we've come up with:
0. Discuss this with your player.
Be open and tell the player that you're struggling to engage all of the party while allowing their character to shine when in its element. Ask them for the limitations they see to the character: any you invoke that came from their mouth will seem inherently "fairer" than those you invoke on your own. Some would call this metagaming, I call it being explicit about the social contract. "We all cleared our schedules, so let's try and make it fun for all to play."
1. Sightlines.
That 600' range (I'm assuming a longbow in this part) can let a sharpshooter get off four or five "free" shots before a foe has a chance to respond. If they have a sightline. Yes, the sharpshooter ignores 1/2 and 3/4 cover. But they don't ignore total cover, which is what's granted by an interposed building, hill, &c. And at 600' off, moving laterally to "see around" a small hill is going to take your sharpshooter some time.
Real-play example: on the road my party encountered some giants wrecking a small keep. I got one shot in, and the giants circled to the other side of the building. While I was circling around to get a look at them the rest of the party snuck into their effective ranges, and the encounter basically started off with giants and rest-of-party at 100', me at standoff range. Only got one "free" shot.
2. Numbers.
That sharpshooter's great at delivering a big punch at a low-AC target. But 25 damage vs. 15 damage is moot to a 10hp target. I understand you can't play too much with encounters' composition (because of AL), but you can play a lot with monster tactics. If the encounter has a mix of big-target and small-target foes your sharpshooter would much rather be swinging for the fences against the big target. So rush them with little targets.
Real-play example: a giant was coming through the forest, but just as we started to see his head a group of I-forget-whats came out 100' ahead of us. I could take my shots at the giant, but a dozen magmin were bearing down on us....
3. Focus on party-mates.
The nice thing about being the sniper is that you stay relatively safe, raining death from a minute's sprint away. The not-nice thing about having a sniper is that the damage your opponents are dealing tends to be concentrated on \$N-1\$ party members rather than on \$N\$ party members. That sniper can't stabilize an ally or drag away a body. It doesn't take too many times choosing to stay safe before you'll see a mate drop and there be nothing to do about it. Choosing to stay at standoff range also chooses to write oneself out of a lot of interactions.
4. Size of strike.
So far these have all focused on the range-portion of Sharpshooter. But what about the size of that strike? I'd claim it's not actually that large, as compared to other characters built to deal single-target damage. For example:
A Sharpshooter (feat) archery (fighting style) Ftr4 can expect +3 to hit & 19.5 expected damage (d10 weapon damage, assuming Heavy Crossbow + 4 DEX + 10 sharpshooter).
A dueling (fighting style) Ftr1/Ro3 can expect +6 to hit & 17.5 expected damage (d8 weapon damage + 2 dueling + 4 STR + 7 sneak attack). (And we haven't even piled a feat onto there.)
A Dual Wielder (feat) two-weapon (fighting style) Ftr4 can expect +6 to hit & 17 expected damage (4.5 weapon damage + 4 DEX, twice).
Now the expected damage per attack between those two will depend on AC, but for many ACs the duelist fighter/rogue or two-weapon fighter is delivering a bigger punch, just as sustainably. In effect, with a sharpshooter you're trading a bit lower damage for safety (from range).
You mentioned how large the damage gets once your sharpshooter grabs second attack and piles on an action surge for a third, but that's. frankly, a red herring. Any fighter build is going to have that "problem"--it's a class feature, having nothing to do with Sharpshooter.
5. And sometimes, let them shine.
Sometimes you'll be fighting a crowd of kobolds in their warren of tunnels, and the sharpshooter'll effectively be mooted. And they'll bemoan the opportunity cost of not taking Sentinel or Polearm Master instead of Sharpshooter.
But every once in a while they'll be standing on a battlement on a sunny day with a clear view to the forest's edge a half-mile out and three giants approaching. With a smile, they'll turn to the party and say "don't worry, I got this. [Aside] 'I love it when a plan comes together.'"