Your very old first generation iPad mini can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).
Apple ended update support for iPad mini in September 2016. Your iPad mini cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed - in addition to which, iPad mini is a 32-bit architecture device, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms.
You need to be aware that compatible Apps for your iPad are increasingly difficult to find - as third-party developers are increasingly dropping support for older versions of iOS preceding iOS11/12. As already indicated by ProustGiulio, the YouTube App already requires a higher version of iOS than your iPad can support.
If you want or need to access most current Apps, requiring more recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model. For YouTube, you do have another alternative - in that you may be able to view content from this portal:
https://www.invidio.us/
Given the increasing difficulty with Apps and compatibility with your old iPad, it now be time to consider replacing your iPad with a newer or current model. Of the current models, even the entry-level iPad7 will massively outperform you current iPad - and is compatible with the vast majority of current Apps.
I hope this information provides helpful clarity as to your available options - and the limitations of your current iPad mini.
