The line "Und unsere Traüme schmieden" actually means "and forge our dreams" and not "our dreams are forging" because
|Wir wollen| ein großes Leben
Im Lichterschein der Nacht
Und |unsere Traüme schmieden|
is just one sentence and "Wir" is the Subject while "Träume" is the object, "schmieden is the Prädikat. If "Und unsere Träume schmieden" was a second sentence it would mean "our dreams are forging" but as it is one whole sentence, "Träume is the Object as "Wir" stays the subject throughout the whole sentence.

Source: I am a German native speaker with a C2 in English.

Thanks for the good translation, just one small mistake I wanted to correct, as it really changes the meaning of the sentence

Edit: Just two more things I noticed: "Und euer Herz berühren" means "And touch your hearts", as "euer" means "your" and "unser" would mean "our". The second thing is, in line 18 something was transcribed wrong, he's singing "Kohlewolken", which means "Coal clouds", not "coole Wolken", which also fits the theme of the song better.