Orsdxy

I'm a DM for the first time and I'm running LMoP with a group of 5 very experienced players.

I have difficulties in handling situations in which the players try to intimidate the enemy roleplaying the intimidation with "scenic effects".
For example, suppose they meet with a random group of goblins which is looking for them.

They usually start casting lots of spectacular cantrips or 1st level spells; like the flame becomes blue, a thunder comes from clear sky, a deep voice from nowhere pretends to be the Maglubiyet the God of Goblins saying to beg on their knees, a little earthquake moves the terrain, and so on. So, since the group of goblins is supposed to be not intelligent, I always feel like the goblins should become submissive, docile, compliant, subjugated, and so they refuse to fight, or they run, or they get to the floor praying, and so on. If the goblins ignore this kind of intimidation, it doesn't feel right to me. And I don't really like the feeling when it seems that the players control my monsters.

What is the best way to handle these situations?

Treat it as a contest

The players are effectively trying to use a level 0 cantrip to produce the same result as a higher level crowd control spell like Fear or Mass Suggestion. Obviously, this is game breaking.

We had an arcane trickster rogue in our group who tried this kind of thing a lot. The way our DM handled it was to treat it as a contest. The caster is trying to deceive the goblins into thinking that they should not attack the party using the effect of a spell.

The caster casts the cantrip and then the makes a Deception or Persuasion skill check against the goblins' Insight checks.

You could have the goblins roll a single combined check or individually. If you do the latter, any goblins that are not convinced by the cantrip's effect can rally its comrades by saying something like "It's a trick! That's not what Maglubiyet sounds like!" (or teaches, whatever).

Rolling like this gives the goblin pack a high chance of resisting the cantrip's intended effect.

Alternatively, you can split the difference and have some of the goblins sit in one place for a round, quivering in their boots, while the unaffected ones charge forward. The scared goblins buck up the following round and join the braver ones.

Doing it this way allows you to keep the solution "within the game." You don't have to have a meta discussion with your player(s) to tell them that you won't let them do something. That's never fun.

Goblins are not actually dumb, unless the ones in Lost Mines of Phandelver have significantly different stats from normal. By default they have an intelligence score of 10, the same as an average person, and an 8 wisdom, which is only slightly worse. They are perfectly capable of recognizing the gestures and chanting of spellcasting and determining that it is a trick designed to intimidate them. They live in a world where illusions and magic are commonplace, so they are far more likely to assume that they are being tricked than that their god is directly speaking with them.

By default I personally would not allow any such attempt to work at all unless the spellcaster both concealed themselves from view so that the casting was not obvious and made a successful Deception check, and even then I would probably only give advantage on the Intimidation roll.

They are trying to intimidate, so they make an Charisma (Intimidation) check

The spells do not do anything other than what they say; however, if you feel that the spells etc. would be advantageous then give them advantage on the check.

Note that this is giving the spells more power than they have, but rewarding good play may justify such house-ruling.