We use the phrase make it happen.
But why don't we use happens since it has the third-person pronoun it?
Make it happens
This is tough!
I think it goes same with let. The only thing I can make out is make or let does not directly involve the third person. Said that, the third person is not doing things but they are indirectly involved, without their consciousness. I'm not sure how to put it correctly in words!
Make him study -he does or does not study, yet
Let her go -she is not directly involved in 'going'
and so on...
All above mentioned examples don't involve the third person doing things directly. The rule is when they do it directly, we apply 's. And thus, when we say "make/let it happen, the it does not perform action directly as the subject.
It goes - a subject doing things directly, by itself
Let it go - Here, the subject does not do things directly
[This is the best thing I could come up with! Native's inputs will be very useful and I'm so curious for their comments!]
Because it is not the subject of the sentence. This is an imperative (a command or directive), given to the listener. The you is ellipted, because it's understood by both parties that the second is receiving an instruction from the first.
These two sentences have the same meaning (when given as commands).
It wouldn't make any sense for it to be the subject of the sentence, if you think about it. The thing that needs to happen usually doesn't have any agency; it can't perform any actions. For example, let it in make it happen mean reach one million dollars of sales. You can see that it makes no sense to say that the sales target should reach itself, but it makes a lot of sense to instruct a sales team to sell a certain amount.
We conjugate verbs in accordance with the agent performing the action. Commands are directed to someone, so they use the you form. It is the object of the command; the thing "receiving" the action, not the thing performing it.
It's because the causative verbs "make", "have", and "let", as causative, go with object + bare infinitive: Causative verb + object + bare infinitive / I will make it happen / I let her go / I will have my dinner prepared (in this case the past participle replaces the substantive form of the verb)
As Juan pointed out in their answer, these kinds of verbs are called ‘causative verbs’ and they take object + bare infinitive. I will mark ill-formed/incorrect sentences with an asterisk (*). Let's analyse the sentence “he made me do X”:
If you're unsure, replace ‘made’ with caused me to:
the second sentence is ill-formed and incorrect in standard English
I'd also like to point out that it's true for ‘make’ only in active voice. The use of to is obligatory in passivised constructions:2:
In the OP's sentence, ‘make’ can be analysed as being cause it to:
this is ungrammatical because we always3 use infinitive after to in present tense, so the correct one is:
When the base form/infinitive is used without to, it's referred to as ‘bare infinitive’ as in I saw him dance (not *I saw him to dance)
See CGEL: ‘Note also that when causative verbs like make and let are passivised, infinitival to switches from being disallowed in the complement to being required’ (p1186).
Well, not always; there are sentences like I'm looking forward to meeting him, where we use gerund after to, but that's tangential to what we're discussing here
'Make happen' is a phrasal verb. Use it in a sentence, 'make it happen' is imperative sentence. Therefore the structure remains to be 'make happen'; not possible to add an s 'make it happens' or 'you make it happens'. 'It' is not the subject in this sentence so as to conform with the third person use of verb. The word 'happen' though it's a verb form which can either be used as transitive or intransitive can function as an adjective in this sense: Make it happen. Make it beautiful. Some Verbs, as part of speech, can function as an adjective or even as a noun. It depends on use.