I don't think there are records of serial numbers and dates of produciton for Standard machines like Singer. You can get an idea if you compare serial numbers to other Standard machines of known date. Another way is to post a picuture of your machine, and someone might recognize the particular model. From cabinets, decals and details on the machine you can often narrow down date production.
There's a bit of info
here, nothing that helps date it, but it is a start. The Standard Sewing machine was in production from around 1880 to 1929, when company was bought up. Production of Standard models were probably kept up until 1934 when Singer bought the company. I found it mentioned on
Sewmuse.
There are a few who probably knows more about the company, and might help identify your machine on the
Victorian Sweatshop, some over there are active here too.
I don't know if older family members can confirm about the ownership of your machine, it tends to be the only source of info like that.