Well, you can be get traffic to your website from facebook group and it will be possible only when will you join relevant groups and you can also try to share your website page link in that particular group.
so when page members sees your link or post in a group and if they found it interesting then they could click on given link.
You can target specific niche groups and post. For example, if you are promoting weight loss products, search for weight loss and fitness groups for posting
In my 20 plus years as a digital marketer, I have used Facebook groups as a source of traffic to my page and my website. Facebook groups are a great place to understand your target audience. Facebook groups essentially contain members who are like-minded and share similar interests. The first thing required to gain followers is credibility and the trust factor. You need to be seen as someone knowledgeable about the topic and willing to help fellow members. Slowly once you have gained a reputation of being a good source, you can start to highlight your blog or site. Here again, do not directly promote your products. Explain as to how using the product might solve their problems. Once people trust you, they will automatically value your opinion and are likely customers. Overpromotion may lead to being banned. Then again here and there subtly hint at it. At the end of the day, do not forget you are there to promote your site or product.
If you have any queries or look to discuss, I am happy to do so.