A novel generative site-specific beamforming (GenSSBF) approach, termed fast beam-brainstorm (F-BBS), is proposed to address the practical bottlenecks of slow beam generation and fixed channel probing lengths in existing GenSSBF. To accelerate beam generation, F-BBS utilizes a two-stage distillation strategy that learns an average velocity field, instead of an instantaneous one, to guide the beam generative process. This strategy enables larger generation steps, realizing few-step or even one-step beam generation. Furthermore, to accommodate flexible channel probing lengths, a stochastic masking mechanism and a beam index-aware masked condition encoder are proposed, enabling a single trained model to operate with variable-length channel probing observations without retraining. Therefore, FBBS achieves the fast generation of high-fidelity communication beams from coarse and variable-length channel probing feedback, i.e., reference signal received power (RSRP), from user equipments. Simulation results on accurate ray-tracing datasets show that 1) F-BBS achieves comparable performance while reducing the beam generation cost by over 90% compared with diffusion-based GenSSBF solutions, 2) F-BBS realizes robust performance across variable channel probing length, and 3) FBBS offers a desirable trade-off between beamforming gain and beam probing overhead.