Learn Turkish: Biz büyük bir ağaç görüyoruz.

The word breaks down into the verb root gör- (see), the connecting vowel -ü-, the present continuous suffix -yor-, and the personal suffix -uz. Because the tense suffix -yor always contains the vowel 'o', the personal suffix for biz (we) that follows it is always -uz.

Why is the word order büyük bir ağaç instead of bir büyük ağaç?

In Turkish, the indefinite article bir (a/an) is placed between the adjective and the noun it describes. So, "adjective + bir + noun" is the standard way to say "a [descriptive] [thing]".

"Tree" is the direct object here. Why doesn't ağaç have an accusative case suffix?

Turkish only uses the accusative case suffix for specific direct objects (like "the tree" or "my tree"). Because we are seeing "a" big tree (an indefinite object), ağaç stays in its plain dictionary form.

Since görüyoruz uses the present continuous (-yor) tense, why does it translate to "We see" instead of "We are seeing"?

In English, verbs of perception (like see, hear, smell) are rarely used in the "-ing" form. Turkish does not have this restriction! Using the -yor tense here is the most natural way to say you see something happening right at this moment.