First, while I understand the sentiment, I never want to be embarresed by any version of the product my teams launch. I prefer to subscribe to the saying "perfect is the enemy of good enough". The point really is, you need to get early versions of your product that are usable in the hands of users quickly, so you can get real world user feedback in order to know what needs to be fixed/enhanced/perfected to gain user adoption and growth.
If you spend too long iterating internally on the product or feature without real user feedback, chances are high that you and your team are wasting time iterating on the wrong things from your buyer's and user's perspective, which is dangerous when bringing new products to market.
However, as a PM, it is important for you to understand the incentives of the company/business within which you are running your product. For large companies, the main focus is on reducing business and user risk, so the idea of releasing products that may not meet the highest QA standards is met with resistance, as expected.
In that case, I recommend using version labels such as "EAP", "Alpha", "Beta", "GA" etc. to set expectations both internally and externally that this is an early verion of the product, *and* that the product will be refined based on user feedback. I've found success with this approach when launching early versions of products and features in larger companies.