Esperamos la llegada.

It can be either, depending on context.

• Present indicative: we wait / we are waiting / we expect
• Preterite: we waited / we expected

This happens because for -ar verbs, the nosotros form is the same in the present and the preterite:

• esperamos = present
• esperamos = preterite

So the surrounding context tells you which one it is. On its own, Esperamos la llegada is often understood as present, but it is technically ambiguous.

Spanish often leaves out subject pronouns because the verb ending already tells you who the subject is.

• espero = I wait / expect
• esperas = you wait / expect
• esperamos = we wait / expect

So Esperamos la llegada already means we because of -amos.
You could say Nosotros esperamos la llegada, but that usually adds emphasis or contrast, such as:

• Nosotros esperamos la llegada, pero ellos no.
  We are waiting for the arrival, but they are not.

Because in standard Spanish, especially in Spain, esperar usually takes a direct object without a preposition when it means to wait for or to expect.

So you say:

• Esperamos la llegada.
• Espero el autobús.
• Esperan a María.

Not normally:

• Esperamos por la llegada.

In some regions of the Spanish-speaking world, esperar por is used, but in standard Spain Spanish, esperar by itself is the normal choice here.

La llegada is a noun meaning the arrival.

It comes from the verb llegar = to arrive.

So:

• llegar = to arrive
• la llegada = the arrival

This is very common in Spanish: a verb and a related noun are often both used.

Examples:

• salir → la salida
• entrar → la entrada
• llegar → la llegada

In this sentence, la llegada is the thing being awaited or expected.

Because Spanish often uses the definite article where English may or may not use the, especially with events, abstract ideas, or when referring to a specific situation.

Here, la llegada means the arrival, usually a particular arrival that speaker and listener understand from context.

Compare:

• Esperamos la llegada del tren. = We are waiting for the train’s arrival.
• Esperamos una llegada rápida. = We expect a quick arrival.

So la makes it sound like a known or specific arrival, not just any arrival.

Not very naturally in this sentence.

Esperar can mean to hope, but that usually appears in patterns like:

• Esperamos que llegue pronto. = We hope that he/she arrives soon.
• Espero verte mañana. = I hope to see you tomorrow.

With a noun phrase like la llegada, esperamos is more naturally understood as:

• we await
• we expect
• we are waiting for

So Esperamos la llegada usually means we are awaiting/expecting the arrival, not we hope for the arrival.

Good question. Spanish uses the personal a only before a specific person (or sometimes a personified being), not before things or events.

So:

• Esperamos a María.
  We are waiting for María.

But:

• Esperamos la llegada.
  We are waiting for the arrival.

Since la llegada is an event, not a person, there is no personal a.

Yes, but it would mean something different.

• Esperamos la llegada = We await/expect the arrival.
• Esperamos llegar = We hope/expect to arrive.

So:

• la llegada is a noun: the arrival
• llegar is a verb: to arrive

This is a very important distinction. Changing la llegada to llegar changes the whole structure and meaning of the sentence.

In most of Spain, llegada is pronounced roughly like ye-GA-da, with the stress on ga.

A few helpful points:

• ll is usually pronounced like the y sound in English yes in most modern Spanish pronunciation.
• g before a is a hard g, like in go.
• The stress falls on the second syllable: lle-GA-da.

So a simple guide is:

ye-GA-da

Some regional accents may pronounce ll slightly differently, but that is the most useful general pronunciation for a learner.

The normal, neutral word order is:

• Esperamos la llegada.

But Spanish is more flexible than English, so other orders are possible for emphasis, style, or contrast. For example:

• La llegada la esperamos.

That sounds more marked, as if emphasizing the arrival in particular.

For a learner, the basic pattern to remember is:

verb + object
Esperamos + la llegada

That is the most natural default version.