How do I have a stronger conviction for an investment thesis?

There are a few subtypes of reasons 

1) usually for fundamental theses you are asking “what do you appreciate that other people don’t appreciate?” Think about what a typical investor does all day and ask yourself whether the fact you know would be likely uncovered in their investment process. If you insight could have been made from reading a single news article, then it is not novel. However, if it is subtle and requires a mosaic of information then it is less likely to have been noticed by others. If you have read anyone else make the argument you are making, then that is clear evidence against your insight being novel. You only get paid if you do work that others are not doing. Sometimes there are related questions too. “Am I doing a service to someone else by doing this trade?” is sometimes a good one for more short-term trades. 
2) The next step is to grade your feeling of knowing something. How do you know that other people don’t appreciate what you know? Is your insight from a credible, primary source? How likely is it that your source is noisy and does not reflect reality? How sure are you about your beliefs of what other investors know? Have you talked to other people about their reasoning? Have you compared your calculations to a recent consensus figure? Separate from certainty is looking at the magnitude of your difference from consensus. How sure are you that your difference from consensus is correct? How much does your difference from consensus matter to the stock? 
3) Next, it’s helpful to think about adverse selection. Do you have as much information as an intelligent market participant over your investment horizon? For example, if this stock trades on credit card data, do you at least have access to that information and you’ve looked at it? How sure are you that you aren’t the dumb person at the poker table? A corollary here is to focus on small stocks since sophisticated investors are less likely to focus here. 
4) sometimes you have no unique insight but the stock is still a good investment. This happens when you find insanely good businesses with remarkable unit economics and a large future opportunity to invest capital at these economics. A company that is cheap does not fit in this category nor does a company that is very above average in quality - it needs to be like top 5% of companies. If you find a company that is Facebook or Netflix in terms of quality but is still $10B in market cap then these are usually good bets. 

It’s honestly great to hear that you think you have no edge! It’s very self aware of you because it’s true. The reason why you feel this way is because you probably have no edge relative to the market. Most likely you have slightly negative or zero edge. Try looking at investment pitches of successful investors to get a better sense for what can constitute edge.