You need to be flexible, use multiple databases, and use the FAN Club method.
Be flexible
What gets put into an index by an indexer in the 21st century is what the indexer interpreted from the digitized copy of the microfilmed version of a document that was handwritten. The handwritten document may or may not be the original; it may have been a contemporary or later transcription of an original.
The original itself in rare cases (e.g. signatures) was written by the person whose name it was; in most cases, it was written by a government official, census enumerator, or clerk who was writing down what they thought they heard.
The information that the clerk heard was not necessarily provided by the people involved. For censuses, sometimes the information was given by a neighbor or a child in the family, who may not get the names and ages exactly right.
Therefore, what you're seeing in the index is not necessarily how the person actually spelled their name. It's a transcription of a fuzzy copy of a possible transcription of what a person wrote down about what they heard from a person who possibly didn't state the correct information.
With that out of the way, one thing to consider in this specific case is that the name may originally have been Bryłski with the Polish letter Ł, which is pronounced like W but in its lowercase form is often mistranscribed as a T. And of course, names that end in -ski are sometimes written down as -sky.
So you may need to look for something that is indexed as Brewsky or Brytski or any combination of
BR + (vowel) + (L or W or T) + SK + (I or Y).
Use multiple databases
We all have our favorite genealogy sites, but they don't all have the same information. Sure, there is a lot of overlap between FamilySearch and Ancestry, but very often I find that one has records that the other one doesn't. That's the case here, where Ancestry has a database called "Milwaukee, Wisconsin, U.S., Births, 1839-1911." FamilySearch, in turn, has records and books that Ancestry doesn't have.
Use the FAN Club method
If you can't find Serafina directly, you should FAN out to look for her Family, Associates, and Neighbors.
Since Serafina was a newborn in the only record you've got, she's not likely to have any associates, but you do have several very useful pieces of information in the document you have. First, you have the full names of both parents. Second, you have the street address where the family were living in October 1910.
Searching the parents, you find a registration of birth for a John Joseph Brylski, born June 18, 1909 to parents with nearly matching names and ages. According to his birth registration, John Joseph was child #2 to these parents; Serafina's birth registration the next year says she was child #3 to her parents.
In 1909 John Joseph's parents were living at 957 Maple. Locating the 1910 census for Milwaukee, we find that it was taken in April, so Serafina would not appear, but at 957 Maple there are listed a Brylski family, parents Joseph and Mary, their sons Zygmunt almost 2 and John almost 1, and Joseph's brothers John and Boleslaws. This is the first marriage for both Joseph and Mary, they've been married 2 years, and they have 2 living children out of 2 born. They are listed as Russian-Polish, speaking Polish; Joseph immigrated in 1906 and Mary in 1907. You may not find this record if you search the index for BRYLSKI, because they've been indexed as BOYLSKI. This is the flexible part.
You say Joseph died in 1917, so he would not be in the 1920 census, but if Mary lived until the 1960s, she should be in the 1920 census. Also, you can search for Zygmunt, who might also appear as Zygmund or Sigmund or another variant. This is where the FAN Club comes in.
The 1920 census shows Mary (a widow), Zygmunt, John, a 6-year-old daughter Martha, and Mary's brother-in-law Boleslaw. This census also shows Mary arrived in 1906 and was naturalized in 1912, so you can look for naturalization papers that may list the number of children she has.
Unfortunately, the 1920, 1930, and 1940 censuses do not have columns for the number of children born and number of children living, so you can't get information about a possible deceased child that way.
Digging a little more into Milwaukee births collection, we find a registration of birth of Siegismund Vincent Brilski, April 20, 1908, parents Joseph Brilski and Mary Andrjeierski (sp?), living at 957 Maple, the same address as on John Joseph's birth registration. So here we have yet another different spelling of both Zygmunt and Brylski.
Martha is another name you can add to your FAN Club. We won't find Martha's birth registration in this collection, because the collection goes only through 1911, and she was allegedly born around 1914. Or was she? Here's where it can be helpful to be flexible. Find out more about Martha. Locate school records, marriage record, 1930 census and later. Was she really born in 1914, or are Martha and Serafina the same child?
Once you have collected names for your FAN Club, try to track down their obituaries. You may get lucky with an obituary that gives a list of "predeceased by" relatives, e.g. "predeceased by his/her daughter/sister Serafina." The FamilySearch Wiki for Milwaukee County (use multiple databases) has tips and links for locating Milwaukee newspapers and obituaries.
Another avenue is to track down where they were buried and check for other Brylski graves in the same cemetery. The St. Adalberts Cemetery in Milwaukee has 10 Brylski graves listed (added by John Brylski, the OP?) including Joseph, Boleslaw, Zygmunt, and John Joseph, but not Martha. If you have physical access to this cemetery, walk around the Brylski graves and look for nearby headstones that are unmarked or marked just "infant."
Summary
- Try to find information about Serafina herself, particularly her death, in vital records, newspapers, obituaries, cemeteries.
- Try to find Joseph and Mary's naturalization papers, to check whether they contain information about children.
- Try to confirm Martha's birth year, to rule out the possibility that she could be Serafina. If you can find another source for birth records and you find one for Martha in 1914, or a newspaper article saying Joseph and Mary just had baby #4, or school records from which you can extrapolate her age, that would put you on the right track.
- Try to find whether Serafina is mentioned in her family's obituaries: her father, mother, brothers, and sister.
