EU passport holders can enter Canada as visitors on their passports. Typically they are given six months (although how long they are given is up to the immigration officer they encounter when they enter the country). Yes - you can request an extension of six months (no guarantee it will be approved).
During this period you can seek employment. Your employer will first need to obtain an approved LMO and then you must obtain a TWP before you can start working.
Note that obtaining work in Canada as a foreing worker is relatively difficult. To obtain an approved LMO, the employer must prove they advertised the job and were unable to find a Canadian to hire or train for the role. For this reason if you have specialized skills / experience - the chances of securing employment are higher. Because the process of hiring a foreign worker takes time and paperwork, you will likely find that many employers aren't willing to consider you as a candidate. However that doesn't mean you can't try.
Good luck.
