I would start with their death record, because I often find it's easiest to work backwards chronologically (death records will be the most recent records and therefore most likely to exist and have the most data) and death records often list the parent's names unless unknown by the informant. And if you know when/where your great grandfather died, this is the easiest record to track down in my opinion. Some death certificate can be found free at www.familysearch.org
but some you may have to order from the state, usually from the Department of Health. If you don't know when he died but you know what state he likely died in, you should be able to find an index where you can look up his death date and order the certificate.
Marriage records sometimes list parents names too. If he married in the US, you should be able to track down a marriage certificate. Again, if you haven't found anything on ACOM, www.familysearch.org
(and again, it's completely free) is the next place to look and if it's not there, you generally need to know not only the state but also the county where he was married to order the marriage certificate. You usually find them from the County Clerk/Register of Wills/Orphans Court.
If you let me know what state/county he likely died/married in, I can probably direct you to the correct websites of where to order the certificates or search the indexes to find the correct date.
The other suggestion of finding his immigration records is also a good one. Even if he traveled alone and there's no mention of a parent back home, it may tell you exactly where in Poland he was born which will help narrow your search down - you may then be able to find Polish records like a birth record with his parents names on it.
Keep in mind that census data can be way off sometimes - in my experience the year of immigration especially is often a year or two off so when looking for his immigration record, be sure to search surrounding years, not just 1907.