ATLANTA — If any National League team appeared built to welcome the arrival of the designated hitter this season it was the Mets. 

Now, with less than three weeks remaining to the trade deadline, if there is one team that could use a DH, it’s the Mets. 

In a season that started with Robinson Cano, Dominic Smith and J.D. Davis as primary options to fill the role, the Mets are now searching. If there is one spot that should be easiest to fill heading to the Aug. 2 deadline it’s that of a veteran bat playing for teams removed from contention. 

The Mets have been patient with Davis in particular, but haven’t been rewarded. Though still among MLB’s leaders in hard-hit ball percentage — he ranks in the league’s 99th percentile — Davis entered Tuesday’s game in Atlanta with a .241/.330/.355 slash line with three homers and 19 RBIs in 191 plate appearances. 

Smith has shown flashes of productivity since his return from Triple-A Syracuse, but overall owned a .248/.310/.429 slash line as play began. Smith’s last homer came last July 21 in Cincinnati. 

“We’ve got among the lowest DH productivity in the game,” team president Sandy Alderson told The Post’s Joel Sherman and Jon Heyman on “The Show” podcast. “Take [Pete] Alonso out of it and it’s been very poor. … We’ve been waiting all season for one or two of those players to ignite, and that hasn’t happened.” 

Davis told The Post he met with general manager Billy Eppler in spring training and was informed he wouldn’t be traded. This after an offseason in which Davis, Smith and Jeff McNeil were possibilities to depart in trades. But Davis said he wouldn’t be surprised if Eppler changes course and trades him. 

“I know that he as a GM has to listen to every [proposal] that is being sent to him and I know his job is on the line and he needs to make the right decisions for the team,” Davis said. “If it happens, it happens and I will get a clean slate somewhere else. But as of right now I am trying to do my best to be a good teammate. Even when I am on the bench I try to look at video, look for any tendencies … look if a pitcher is tipping. 

“I can’t really worry about playing time, my mechanics and the trade deadline, all three, or I am going to just get consumed with kind of a negative cloud, so I don’t really want to go down that road or get distracted when the team needs me out there to compete.” 

Trey Mancini (although the Orioles have played better lately and might not necessarily be sellers), Nelson Cruz, Josh Bell and Andrew Benintendi are all names that could make sense for the Mets, who will have to decide to what lengths they will go in terms of prospects to upgrade the lineup. Top prospect Francisco Alvarez isn’t going anywhere, and the Mets have a rich next layer that includes players such as Brett Baty, Ronny Mauricio, Mark Vientos and Alex Ramirez. 

“I don’t think we’re at the point where we know what the cost is going to be for an outside solution,” Alderson said. “We’ll just have to see. Part of it is going to be, what is the marketplace? Who’s out there competing for a DH? Those teams don’t come immediately to mind.” 

Alderson also ruled out the possibility Alvarez, who was recently promoted to Triple-A Syracuse, would immediately be considered for a DH role with the team. 

“In order for him to be considered, we’d have to see sustained performance over some period of time at Triple-A,” Alderson said of Alvarez, who is hitting .125 in five games since his promotion. “We haven’t seen that because he hasn’t had the opportunity to do it. But I would say that’s not an immediate option.”