I live in Echo Park and worked downtown for several years (commuting by bus), and depending on your willingness to take the bus, the 2/4/704 and 92 bus lines will take you pretty much anywhere from the main hubs of Silver Lake and Echo Park into downtown.
I would not recommend using Google Maps’ transit feature to find bus arrival times as I have found it to be buggy and it goes off of Metro’s published schedules, not real-time arrival (even though it’s supposed to!). Use nextbus.com or the nextbus app instead.