The Scottish Championship winners face the Blue Toon in the opening round of Premier Sports Cup ties.
The Jambos then host Cove Rangers on Tuesday and Neilson is mindful of the demands on individual players.
"It is very, very early," the Hearts boss said. "But to be honest, it is good to get back at it.
"Sometimes pre-season can be quite long and laborious. You want to get back to the competitive games and so we are looking forward to the games coming up.
"Obviously we want to win every game, so we will put out a team to win every game.
"We play Saturday then Tuesday in competitive games, which is quite early for everyone, and then have a wee break and go again Tuesday then Saturday.
"We will utilise the squad as needs be to make sure we win the games."
Two matches have fallen foul of Covid-19 outbreaks, with St Mirren awarded a 3-0 win over Dumbarton and Forfar the same result against Ross County.
That leaves Hearts and Livingston as the only top-flight teams in action on Saturday, with last season's beaten finalists travelling to Brechin.
Kilmarnock, relegated from the top flight last season, are away to East Kilbride, while there is a Fife derby between Cowdenbeath and Raith Rovers.