I would like to know if it is possible to gain access just for a little while because it is very urgent )):
If not, is there any other way aside from waiting for 24 hours?
Also I don’t exactly know why or how I hit my CPU limits. Is it related to my activities outside of the website?
No there is not, there’s not other choices but to wait.
In the Client Area there should be a knowledge base article link attached for you to read to learn more about your suspension and how your site has utilized 100% of your CPU usage.