Start with whatever is easiest for you to find, take lots of notes, and build a case.
If you have a family tree program on your computer, use that. I recommend recording every single fact you have, even ones you think are wrong. Create sources for every place you got information. I even have sources that I call "Family Lore" (with subsets for surnames/families). I suggest one of your sources is your birth mother. This way you can record everything she tells you but have it labeled as coming from her. So if you find something that contradicts it, you will know that her version is less authenticated.
As you find more facts about this man, go back to earlier searches that were fruitless and see if you have more luck. Also use new facts to validate other facts you're unsure of.
Take note of everything. Even an address plus a year can be invaluable in determining if a document is for the right person of that name.
If possible, I would try to get your original birth certificate. I don't know the adoption rules for Canada or the UK (not sure where you were born as you don't say in your original question) but you might have luck there. If it gives your birth father's name, you might get a better spelling or a middle name, things you might not have now. It may even give a date of birth and place of birth. The exact date is very useful for narrowing down documents and the town where he was born might be essential.
Go through all the Canadian records you can. Ancestry.com has a fair number, most of which require a Canadian subscription or an international one. In many places (the US for sure), you can access Ancestry's international database for free from a library. Also try Family History Centers and national research centers (in the US this is the National Archives). FamilySearch.org is another place to search and the FHC's can help with information that might not be indexed online.
Go through phone directories in Cambridge in 1960-1, plus some earlier and later. This will give you addresses, timing of his stay, preferred name, and sometimes an occupation. If searching online, check out all of Ontario in case he moved around or lived in a neighboring town.
Ancestry and other places have incoming ship and airline manifests for passengers arriving in Canada. You might get lucky here. While there are some manifests for Hamburg, Germany, in general there aren't really saved manifests for arriving in Europe, or leaving North America, though that might vary.
Do newspaper searches in and around Cambridge. He could be mentioned for all sorts of benign things, or maybe he got in trouble.
If he stayed in Ontario (or at least in Canada), you have a chance to find naturalization records, voting roll information, etc.
Don't dismiss any fact. It may be the key that opens a door later.