Fixed-graph recurrence conjecture for simple random walk on growing subgraphs

Let $\bmathbb{G}_\infty$ be a fixed graph of uniformly bounded degrees on which simple random walk is recurrent, and let $\bmathbb{G}_t$ be non-decreasing subgraphs with $\bmathbb{G}_t\uparrow\bmathbb{G}_\infty$. Fixed-graph recurrence conjecture. Simple random walk on $\bmathbb{G}_t$ is recurrent for any choice of such non-decreasing $\bmathbb{G}_t$. This is presented as a consequence of the monotonicity conjecture and would imply recurrence for simple random walk on every non-decreasing subgraph evolution in $\bmathbb{Z}^2$. The claim remains open in the source.