Back when Borderlands 1 was released, it had a preorder bonus for consoles from certain retailers called the "Gearbox Weapon Mercenary Pack", that granted two starting Gearbox weapons to each character.



While it was never officially released on PC, the content was included in the game, and could be activated, as shown in this guide:
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=429048432
After some testing, I can confirm that the content is still there in the Enhanced Version, and it can be activated in a similar fashion.

To do so, you just need to locate the following ini file:

\Steam\steamapps\common\BorderlandsGOTYEnhanced\WillowGame\Config\DefaultGame.ini

Open it with a text editor like Notepad, and near the end of the file add:

[PromotionalUnlocks]
+UnlockId=1

So it looks like:

; bsg-rwong (11.15.17): DLC cooking - these used to be in DLC ini files... just putting them all here since we're packaging them all together anyway
[DlcPackages]
+DefinitionPackageId=1
+DefinitionPackageId=2
+DefinitionPackageId=4
+DefinitionPackageId=8

[PromotionalUnlocks]
+UnlockId=1
; bsg-rwong (11.15.17): end

When you start a new game, first time you open your backpack you should get the following message:



Depending on your character, you should get:

Brick's RF-BIA Repeater


Brick's SG10-XX Angry Shotgun


Lilith's TK4-BIA Bad Repeater


Lilith's TD22-OP4 Relentless SMG


Mordecai's BLR4-BIA Cruel Swatter


Mordecai's LB30-BIA Vicious Thunder


Roland's BLR-BIA Bad Repeater


Roland's CR30-BIA Deathly Stomper


So you can start a game with up to four Gearbox weapons, two from this pack and two from the Loyalty Bonus (you get randomly 2 out of 6 possible weapons).