The Warriors opened their campaign with a bonus-point 26-20 victory over Munster at Thomond Park and will look to build on that result when they welcome Ulster to Scotstoun on Saturday evening.
Glasgow's schedule sees them finish the regular season with successive away matches against the Bulls and Sharks in South Africa, and defence coach Scott Forrest says that run-in has helped sharpen the focus on collecting points early in the campaign.
"When you look at our run of fixtures, we've probably got a target where we want to do well early in the season," said Forrest.
"We don't want to be getting to the last two regular-season games where we need to go to South Africa and pull results out to finish at a certain point for home advantage, whether it's quarters or semis or whatever that is.
"The stronger we are at the start of the season, the more you give yourself a little bit of a buffer at the end of the season with those two tough fixtures."
The approach represents a slight shift from previous campaigns, when the opening rounds have at times been treated as an extension of pre-season as Smith looked to build his squad into the campaign.
Five points on the road against Munster represented an encouraging opening, with Glasgow recovering from a difficult start at Thomond Park to secure maximum points.
Forrest was pleased with the way the Warriors grew into the contest, particularly given it was the first competitive outing of the season for the majority of the squad.
"Overall, pleased," he said.
"For the majority of those boys, that was their first run-out of the season, compared to Munster, where pretty much all their boys had played in either one or both of their pre-season games.
"There are going to be certain elements of rustiness around what you do. I thought we were stress-tested in terms of our defence, which is what we wanted, especially around that yellow-card period when Ollie was off the pitch in the first half.
"I thought we improved as the game went on. We saw an impact from our bench in the second half. Overall, for a first run-out, we're pleased with where we are."
Attention now turns to the first home match of the campaign against Ulster, with Glasgow looking to maintain the Scotstoun record that has played a major role in their success in recent seasons.