Learn Dutch: Het project zal vooruitgaan als er geen tegenstand is. - The project will progress if there is no opposition.

Because als (if) introduces a subordinate clause, which is a dependent part of the sentence. In Dutch subordinate clauses, the conjugated verb gets pushed all the way to the end. So the structure is literally "...if there no opposition is."

What is the literal meaning of vooruitgaan and why is it written as one word here?

It is a separable verb made up of vooruit (forward) and gaan (to go), so it literally means "to go forward". It is written together as a full infinitive here because the auxiliary verb zal (will) has already taken the main verb position earlier in the sentence.

This lesson covers ondanks (despite). How would we rewrite this to say "The project will progress despite the opposition"?

You would say Het project zal vooruitgaan ondanks de tegenstand. Because ondanks is a preposition, it simply takes a noun phrase after it (de tegenstand). You no longer need a full subordinate clause with its own verb like you do with als.

What is the function of er in this sentence?

Just like in English where you say "if there is", Dutch uses er as a placeholder subject when introducing an undefined or general noun. Here it introduces the concept of geen tegenstand (no opposition). Without er, the grammar would feel incomplete.