There are two main challenges in document-level event extraction: 1) argument entities are scattered in different sentences, and 2) event triggers are often not available. To address these challenges, most previous studies mainly focus on building argument chains in an autoregressive way, which is inefficient in both training and inference. In contrast to the previous studies, we propose a fast and lightweight model named as PTPCG. We design a non-autoregressive decoding algorithm to perform event argument combination extraction on pruned complete graphs, which are constructed under the guidance of the automatically selected pseudo triggers. Compared to the previous systems, our system achieves competitive results with lower resource consumption, taking only 3.6% GPU time (pfs-days) for training and up to 8.5 times faster for inference. Besides, our approach shows superior compatibility for the datasets with (or without) triggers and the pseudo triggers can be the supplements for annotated triggers to make further improvements.