I've known such men. They like the idea of being married and having kids until they marry and have kids and then they immediately want to be single and have no responsibility.
Such men think nothing of evading their obligations such as child support by using other names. As long as he worked at some point he would have gotten a Social Security number. Unfortunately his name does not appear in the Social Security Death Index. This could be because he isn't dead yet or his death was never reported to Social Security or he never collected Social Security. It might help if you knew what kind of work he did (if any kind in particular).
Without any real knowledge of when or where he was born you're going to have a much tougher time of it. He may or may not have been born around the same time as Grace although he most likely was. It does help that you know is full name. But in order to get his birth certificate you will probably have to pay for an extended search which costs 34 dollars rather than 10 and you have to hope you get the right person. Even if you find any record anywhere that has the right full name you still can't be sure it is him unless you later find some other record such as his obituary with some familiar names. This leaves you at square one.
As I suggested the other possibility would be to track down one of his marriage records. If you have any idea where he married you could send for the record. I would start with where he married Grace. If you don't know that start with where your father was born (which was?). In Pennsylvania marriage records are recorded at the county level which means you might have to check several counties in the area and hope they hadn't run off to get married elsewhere.