Technically, no.
There are a lot of misconceptions related to Tinker's Tools, and they were actually relevant to a character I just started. Tinker's Tools are actually a lot more mundane and useless than most players believe.
Many players believe that Tinker's Tools allow you to create simple machines or work on grand devices on a project, but the actual use of Tinker's Tools is to be a medieval, mundane handyman. A few things that Xanathar's Guide to Everything mentions include doing shoddy repairs on a sword, fixing the leg of a table, or patching a hole in a cloak.
Even with a 20 DC, the best you would be able to do would be to temporarily create an improvised item/upgrade (like an improvised shield out of wood).
The "adventurer" benefits of Tinker's Tools come from outside sources, such as a Gnome's racial trait, the quicksmith feat in the Kaladesh article (not exactly Tinker's Tools, but almost identical), or the Gunsmith bonuses from the Gunslinger archetype.
These are not the default, and without those sources, a player should technically not be able to utilize Tinker's Tools to create, but only to repair. And those things you repair should be things common to the lowest fantasy settings possible.
However, ask your DM if this is something you want.
I asked mine, and he allowed me to replace my background with one that duplicates the Gnomish Tinker's Tools traits, along with several other Gnomish-esc things. At the time, he was under the impression that the advanced abilities of Tinker's Tools were inherent, until I basically gave him this same answer.