My favorite tool when it comes to puppies is a leash/long line. Basically for those first 4-6 months if my pup is out of the crate they are on some sort of leash or line, even indoors.
Indoors it provides an easy way to grab them to run them outside to potty, especially if you don’t have a fenced yard. This prevents a lot of accidents when timing is so important for the tiny pups. It also allows you to get ahold of your pup quickly when they snag something you don’t want them to have. You can also work on short obedience sessions super easily during the day or correct those barky, land shark, jumpy moments all puppies have.
Outdoors I utilize all sorts of long lines and leashes. Not just for walks but also for romping and exploring. It allows my puppies the ability to play freely but still be safe. Many say you shouldn’t run with your puppy, and while that is true for on leash pavement human run type of running… I don’t usually put many limits on free running as a puppy is able to change paces and jump and climb which is all good for building strong muscles and joints. SO let them run, but do it safely.
I use a variety of long lines when we are out, it depends on the terrain and the dog usually. I tend to make my own so I can mix up lengths and diameters too. Stores like Home Depot and Tractor Supply sell all sorts of ropes and snaps to make them out of which work out a lot cheaper in the end.
One of the biggest reasons I use long lines is to reinforce a recall, even outdoors at a distance. This allows me to lay a strong foundation very early on and a solid history of success. My big rule with a formal recall command like “come” is I never ask for it if I don’t have a way to reinforce it.
So if you are having a hard time catching your puppy, or allowing them safe romping and exploring time go buy some rope and a leash snap and make yourself a long line or leash. If your puppy thinks this new leash is super fascinating just redirect and interrupt them, the novelty will soon wear off when they find better things to enjoy during their new found freedom.