Does a 300 Watt Inverter need to be directly connect to the battery?

I want to put in a 300 watt or higher draw power inverter in my Sonata 2007 NF. From the fuse box looks like the actual cigarette lighter only has a 25A fuse (on 12V that is exactly 300 watt).

So, can I actually continuously draw 300 watt of power through the cigarette lighter safely without melting or causing a fire? Has anyone actually tried this successfully?

Otherwise, how easy it to get a wire to battery? I have limited experience in car electronics and haven't done any major electrical work on the car before. :confused:

Thanks in advance!