No. When respirators are used to protect workers from airborne hazards such as dust or pollution, employers are legally required to undertake fit-testing (see for example the US Occupational Safety and Health Administration fit-testing standard). But even non-fit tested respirators will provide superior protection over cloth or surgical masks.
A respirator should rest against your face with no gaps, especially around the nose and chin. To create a tight seal, form the nose clip and place both straps around your head, adjusting them if necessary.
If the facepiece collapses a small amount when you inhale, the respirator probably fits well. Get in the habit of doing a “self seal-check” before each wear.