To get the second meaning:

Le mariage n’est plus que dans un mois, mais les gens ne parlent déjà que de ça.

In this case, plus is a comparative, “n’est plus que” insist on the short delay.

You might use donc instead of déjà, however do not use both ” … donc dèjà …”

The ambiguity exists in English with “only” as well. To get the first meaning unambiguously, you’d say

Le mariage n’est encore que dans un mois

And for the second one:

Le mariage n’est plus que dans un mois

PS: “wedding” is probably what is meant here instead of “marriage”