I understand that 'BIG' means different to different individuals. Here by 'BIG' I mean life-changing money (bigger than 20x of your monthly income).
1. Let the money sit in your bank account (wallet) for at least one month. It will allow you to settle down your heightened emotions. Just let the amount sit and do not do anything with it for at least one month.
2. Go on a low-cost, week-long vacation with your family and friends (do not tell anybody about your winnings; do not boast) immediately. It will help you make your relationships stronger and will certainly help in doing step 1.
3. Do not change your lifestyle immediately, as it will help you to remain disciplined, which will eventually help you out to earn even more.
4. Invest in a diversified portfolio other than gambling, probably for the long term, at least 80% of your winnings.
5. If your winnings are even greater and allow you to quit your job, then use your time to learn finance.
If you have any suggestions feel free to addon.
Controlling your emotions after a big win is what a lot of people don't have, the surprise and sudden shock that comes with a big win is not something you can easily control especially if you don't have strong emotional maturity, because different thoughts will be coming to your mind at the same time. Just as you've said OP, the best thing to do is allow the money stay in your wallet for at least a month, then if I'm the one, I will sincerely look for a financial expert, that will guide me properly as I make my investments.
Of course staying low key will definitely help you, as it will make you remain focused without much distractions, because hence you begin to tell people about your current financial status, a lot of persons will be bugging you with their financial issues, even when they don't have one, they will just want to help to embezzle your money.
Emotional discipline is very important when it comes to gambling, I stumbled on a story of a gambler that won his first millions and due to the shock or overexcitement he ended up dead. Not knowing how to manage your emotions properly can put you under the huge risk of having health issues. Keeping the money in your possession for a month isn't really a good idea because as a gambler you will always try to gamble more, this can make you lose your winnings. Immediately you get that money do something with it.