So in addition to the two solid cylinders passing through the domain parallel with the z-axis, there is a diagonal cavity in the domain and that won't give good inflation.
What I find odd is that the diagonal cavity is free-standing in the fluid domain. It does not connect with any wall. How is that possible? Is that an object floating in the fluid?
Regardless of that doubt, I suggest you divide the domain into multiple bodies. Create a cylindrical surface around each cylinder so a tubular cross-sectional body is created. Use the Share button to keep all the pieces meshing without needing any contact. Hide the "swiss cheese" body that had the tubes cut from it. You can define inflation independently on each tube body. Right click on each tube and Mesh Selected body. Once you have nicely meshed inflation on the three tubes, you can mesh the "swiss cheese" body.