Thank you for your question and Welcome to our community :-)
First of all: Congratulations on your job offer, that sounds like a very good opportunity.
You mentioned that you already went to a visa office but didn't get any answer - did you let them know that you already have a job offer and it's time sensitive?
I did some research and found this website, "Make it in Germany", which provides a lot of information on visa for work (including the EU Blue Card): https://www.make-it-in-germany.com/en/visa/kinds-of-visa/work/
This is what they say on their website:
"If you have a job corresponding to your qualifications, under section 18 (4) of the Residence Act you are on principle entitled to a “residence title for the purpose of taking up employment” if the Federal Employment Agency has approved your employment. You do not need to apply for approval yourself. As soon as you have a job offer, just talk with the Germany embassy which is responsible for you if you are still abroad. In Germany you can get further help from the foreign nationals' registration authority or the welcome Centre in the town where you live."
I understand that you do not have a university degree, and I believe that it plays a role here. Fact is: you have work experience and you already have the job offer, that should definitely be taken into account. As they mention in the quote, you can reach out to the Foreign National's Registration Authority or the Welcome Center of your area to find out more about your options to switch visa types, as you do not have said university degree, but a job offer.
Here is information on residence permits for work in Germany by the Berlin service website: https://service.berlin.de/dienstleistung/305304/en/
And by the BAMF: http://www.bamf.de/EN/Willkommen/Aufenthalt/WichtigeInformationen/wichtigeinformationen-node.html
I hope I could answer parts of your question and recommend reaching out to one of the mentioned facilities for more information. Feel free to contact the community again if you need any further assistance!
All the best,