However, I still don’t feel fulfilled for doing so, instead I feel the need to donate time and effort to see the outcome rather than asking someone else to do so.

It is interesting though in some respects. Although it doesn't quite work this way:

let's say you earn 100 dollars an hour but to hire a worker it costs 10 dollars an hour. That means if you donate an hour of your time, it will cost 100 dollars but be 1/10th as effective. It also means that the 10 dollars salary doesn't go to the 10 volunteers, which is a potential other factor to consider considering the types of people who might be volunteering. Of course there are various emotional things at play in there too.

There is a guy named William MacAskill who does the effective altruism thing. If I remember correctly he gives 90% of his wealth away to various charities. He works a well paying job. Some people have a very good skill of making money, so it might be in the best interest of their charitable endeavours to spend their time working hard for money, rather than donating their time to charity. It would mean that they would have to come to terms with the problem you describe though to feel that there is meaning.