Program verification relies on loop invariants, yet automatically discovering strong invariants remains a long-standing challenge. We investigate whether large language models (LLMs) can accelerate program verification by generating useful loop invariants. We introduce Quokka, an evaluation-oriented framework for LLM-based invariant synthesis that provides sound evaluation and achieves state-of-the-art performance. Unlike prior work that treats LLM outputs as noisy symbolic material requiring substantial post-processing, Quokka adopts a simpler and evaluation-centric design that directly validates whether each LLM-generated invariant helps prove the target assertion. We construct a benchmark of 866 instances derived from SV-COMP and evaluate 9 state-of-the-art LLMs across multiple model families. We demonstrate that supervised fine-tuning and Best-of-N sampling yield measurable improvements, and we show that Quokka consistently outperforms prior LLM-based verifiers. Our code and data are publicly available at https://github.com/Anjiang-Wei/Quokka