In general, you can't do this. Even if you convert the VGA to HDMI, you're not getting any sort of increase in quality, it only helps with compatibility (if neither of your monitors has a VGA etc).
The best recommendation would be to find a cheaper GPU - even if it only has a single HDMI, your other options will likely now bw DisplayPort and DVI, which are high quality than VGA and easier to convert into HDMI. GT1030 or GTX1050 run from £90 to £150 I think, and should give you a boost over most integrated options. The 1030 is available as a passive card which means no additional noise from fans, but I have a 1050 with a small fan in one box and can't hear it.
The only other idea that occurs to me is if your PC is new enough to have an integrated USB-C connection as you can find docks and hubs that will fit that which include HDMI.