First, some pointers in a summarized article about verb-first sentences in Spanish.

• The verbs of existence haber and existir go before their subject more often than not.
• Verbs often come before the subject in questions.

The kind of example you gave (Vienen muchos...) is a bit tricky, but I think what's happening there is that the situation is similar to that of a predicate of existence.

If you said Muchos vienen..., then those muchos would be the topic of the sentence, i.e. what you want to talk about.

If instead you choose to say Vienen muchos..., then the implication is that you just want to describe the situation as a whole, as a matter of fact, without introducing a new topic. In English you would do this by using an expression of existence or event. That is, you'd present the situation

Vienen muchos inmigrantes a trabajar…

as one of

• "There are many immigrants coming to work…"
• "It so happens that many immigrants are coming to work…"

This same principle marks the difference between

1. Los inmigrantes comenzaron a llegar ayer.
2. Comenzaron a llegar ayer los inmigrantes.

No. 1 is a statement about the immigrants; no. 2 is a statement about the fact that the immigrants have begun to arrive.

I could give many more examples. Checking newspapers' headlines right now, I'm finding things such as

• Asumió Vizcarra como presidente de Perú. (Some guy called Martín Vizcarra has just assumed the presidency of Perú; the verb goes first because the headline highlights the fact of the assumption itself, rather than what Vizcarra has done or said.)
• Tras el calor, llegó la tormenta. (It's been unseasonably hot but a storm has just come over Buenos Aires; the arrival of the storm is the news, not "what the storm did".)

First, some pointers taken from an article about verb-first sentences in Spanish.

• The verbs of existence haber and existir go before their subject more often than not.
• Verbs often come before the subject in questions.

The kind of example you gave (Vienen muchos...) is a bit tricky, but I think what's happening there is that the situation is similar to that of a predicate of existence.

If you said Muchos vienen..., then those muchos would be the topic of the sentence, i.e. what you want to talk about.

If instead you choose to say Vienen muchos..., then the implication is that you just want to describe the situation as a whole, as a matter of fact, without introducing a new topic. In English you would do this by using an expression of existence or event. That is, you'd present the situation

Vienen muchos inmigrantes a trabajar…

as one of

• "There are many immigrants coming to work…"
• "It so happens that many immigrants are coming to work…"

This same principle marks the difference between

1. Los inmigrantes comenzaron a llegar ayer.
2. Comenzaron a llegar ayer los inmigrantes.

No. 1 is a statement about the immigrants; no. 2 is a statement about the fact that the immigrants have begun to arrive.

I could give many more examples. Checking newspapers' headlines right now, I'm finding things such as

• Asumió Vizcarra como presidente de Perú. (Some guy called Martín Vizcarra has just assumed the presidency of Perú; the verb goes first because the headline highlights the fact of the assumption itself, rather than what Vizcarra has done or said.)
• Tras el calor, llegó la tormenta. (It's been unseasonably hot but a storm has just come over Buenos Aires; the arrival of the storm is the news, not "what the storm did".)