It’s not about being possible or not, but about the quality of the end product- test software in your case.
Could you build your company’s product from scratch ? you probably could, but it wouldn’t be very good or successful.
“Automated testing framework” is a project like any other project, you can quickly hack something as proof of concept but if you want it to be useful you need to plan and architect it properly, and this requires experience.
When you choose a tool you need to consider the common -ilities (extend-ability, usability, maintainability, etc.), limitations and benefits of the tool (no-programming tools are usually limited in applying test logic), needed resources for your future needs (budget and personnel) and other things as well.
What to do then ? it’s hard to say, if you are talented, willing to learn and most importantly have supporting managers you can take a risk and take the project. Otherwise ask for help, it will be for your own good in the long run.