Hi,
"Vers la soirée" would only make sense in a very limited number of contexts. Can't think of any at the moment.
"Vers la fin de la journée" - is that where you were headed?
Otherwise, maybe those can help -
"La journée tirant vers la fin"
"Alors que la soirée commençait"
"Alors que s'annonçait le soir"
"Aux dernières heures du jour"