I am absolutely no expert at dating quilts or hand work, but the bears faces and the style of embroidery remind me of 1950's. I say that because that is the time frame when I learned to embroider. The flower petals stitches remind me of the "bazillion" pillow case edges that I did. My mom would buy iron transfer patterns, iron the pattern to the border of the pillow case and hand them to me to embroider. The styles are very similar.
You now have two suggested ages, does one of them fit your age? You have some good ideas particularly looking at old photographs and talking to older family members. What a fascinating mystery you have to solve this year!