Tiagra lever extremely stiff on new bike
As mentioned in comments you should take the bike back to the store and get them to fix it. I wouldn't even attempt a repair because disassembling anything introduces the possibility the store will decide you caused the problem.

However, initial steps for diagnosing the problem if you want to:

I think it's highly unlikely the that cable routing is the problem because the cable would hang up on both up and downshifts.

You can easily determine if the shifter or derailleur is the problem. Detach the cable from the derailleur, work the shifter. If downshifting is now free the dearilleur was the problem. If still stiff it's the shifter.

You can also attempt to manually move the derailleur from the smallest sprocket to the largest while holding the rear wheel off the ground and pedaling (you need a work-stand or a friend to do this, or possibly put the bike upside down on something that will not scratch the saddle or hoods). Be careful not to catch your fingers in the chain.