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.