These were her firstborns. We all know who Perospero is, and Compote is the minister of fruits at Whole Cake Island. Comparing them to Streusen when he was young highlights some similar traits between them. Thus, implying Streusen might well have been Big Mom’s first husband. And thus the father of Perospero and Compote.
And for those saying that this might not have been possible due to Big Mom abandoning her husband, one has to think that Streusen is an incredible chef and the co-founder of the crew, so it would make sense if she overlooked this and let him stay as head chef. Now, let us compare Streusen and Perospero, they both have long tongues and they both laugh like “Ku Ku Ku”. Even their eyebrows are similar as well and that certainly proves that Streusen was Big Mom’s first husband. Now, coming to her second husband. It could well be Kaido as they know each other for a long time.