MSNBC reporter Cal Perry was questioning Andrew Yang about the Trump budget, and said, “What are your thoughts right out of the bat?”  This is a mashup of “right off the bat” (immediately) and “out of the gate” (from the start).  “Off the top of (one’s) head” (initial thought or reaction) might also be in the mix given the context.  A big thanks to Frnak King who heard this one and sent it in.