You can't. At least, not officially and not easily, at the moment.
There is no current giveaway of promo/gift codes for SteemMonsters Starter Packs. At least, none that are officially coming from SteemMonsters. So, the only way to get the promo/gift codes for a Starter Pack is through unofficial channels, meaning user contests, buying them from other users, or as gifts from users who received the official and limited promo/gift codes.
You're right in saying that SteemMonsters produced a promo/gift code for SteemMonsters Starter Packs. However, as far as I know, these promo/gift codes were only distributed twice and to a limited number of users. So, their numbers are pretty small and the people who have them are probably not willing to part with them easily or cheaply since they are not easy to come bay.
The first distribution was to the backers of the SteemMonsters Kickstarter promotion. These people were emailed promo/gift codes to redeem their Starter Pack and get their special edition cards. Keep in mind that this was not a free distribution. The Kickstarter backers had to pay at least $25 for the SteemMonsters bundle that included their Starter Pack. One backer even shelled out $5,000 for their bundle. The second was to the attendees of SteemFest 3, who received codes from the SteemMonsters teams. Again, this is technically not a free distribution, either, because you'd have to consider the fact that those at SteemFest already spent for their tickets to get in.
There might have been other distributions I'm not aware of, but I am certain that there has not been a mass or completely free distribution of any kind, yet. So far, all official distributions have been limited to specific events. And, in case of the KickStarter promotion, the distribution was limited to those who paid for it.
Why is this the case? Why hasn't there been a mass distribution of Starter Pack promo/gift codes?
SteemMonsters Cards are non-fungible tokens. And every card included in the Starter Packs and the Booster Packs are cards that will be taken out of the entire supply of SteemMonsters Cards, which are actually limited in number. So, the promo/gift codes are not your everyday "freebies" that anyone can use. And, every "free" Starter Pack is not really free. Someone actually pays for it, either the SteemMonsters Team who will take these cards away from their total, limited and pre-determined supply, or another user who will give them up for you.
That's why, right now, the only way to get those promo/gift codes is by winning it in a contest like this one from 18 days ago: (https://steemit.com/gaming/@slobberchops/steemmonsters-starter-pack-giveway). Note that the organizer of the contest received his promo/gift code from SteemFest 3. The problem is, these giveaways are rare. After all, as I mentioned above, the number of promo/gift codes distributed is limited.
With that said, there is a possible alternative to promo/gift codes. And that's through Starter Pack giveaways--not for a promo/gift code but for a new SteemMonsters Account with a Starter Pack already included. In this case, the organizers of the contest will basically buy you in as a prize. @simplymike has contests like this. You can see one of them here: (https://steemit.com/steemmonsters/@simplymike/48-hours-contest-can-t-afford-a-steemmonsters-starter-deck-this-is-your-chance-to-start-playing). His latest one has ended, but a new one might be on the horizon as the 4th Season of SteemMonsters are about to begin soon.
So, the odds of getting one of the Starter Pack promo/gift codes are pretty small because these promo/gift codes are limited in number, to begin with. However, as someone who has been playing SteemMonsters, even for a short while, (I only started during the current season) I can tell you that the $10 Starter Pack is worth it, especially if you want to play the game. This is because of the generous Tournament Prizes and Daily Quest Giveaways. First, all players--even those who only have the Starter Pack--could earn up to 2 Booster Packs every 24 hours by completing their daily quests. And for those who already have the hang of it, you can even win more booster packs as Tournament Prizes. So, the $10 buy in is not that bad. You might be able to earn them back as Booster Packs and in sales of individual cards, pretty quickly.
How do you get the $10 USD to get started?
Well, why not try earning some STEEM by answering questions at Musing.io? This platform currently gives away one of the most generous upvotes in the Steem Ecosystem. So, if you have expertise on some topics, or even if you just like to give your opinion, you might be able to find questions being asked here that you can excel at answering. Answers don't have to be long (like this one), but they have to be relevant the question and helpful to the person who asked. So, who knows, a few upvotes from Musing.io and maybe you could be ready to buy your SteemMonsters Starter Pack yourself. Plus, you would have helped answer someone's question along the way, too.
Hope this helps.
The easiest way to get the steem monster starter pack for free is by participating in steem monster constest. such contests abound in steemit. If you're lucky to win such contests, you will win even more than the starter pack. Also, you can participate in the steem monster discord server and stand a chance of getting some free packs if you are very active there.