The safest way (perhaps even the most effective way) is to try and launch your website as 'Beta', or perhaps as a soft launch. But before you do that, have your entire team run usability tests on the website, irrespective of their role in the website. You can exclude the Quality Assurance Experts and Testers for this.
The main intention of this is to try and break your website, and fix the issues before it goes live. It is far less embarrassing if it breaks before production.
Have your website made live for your organization's internal server and ask everybody in your organization (or atleast a few many) to try and break it. All websites will break atleast a dozen times, but that is a good thing. The more you fix, the lesser chance of it to break when it goes live and made available to the public.
Next thing you can do is to get a few people, who you know personally, or via your team/ organization, and run usability tests on it. You can increase the radius of users with successful fixes, step by step.
You can also set up a 'Bug Bounty' program, to attract more people to try and break your website. Set up a contest with attractive prizes and keep it lit. You don't have to spend too much on the rewards. Try gifts like Amazon Vouchers and stuff like that.
After you release it live, the ideal case is 'zero' bugs. But this isn't practical. Learn from each issue and come up with better versions.
As Edison said, 'I have not failed. I've just found 10,000 ways that won't work.'