I thought the DPS5020 had screw terminals?
For low voltage DC stuff, if the feed is fused or otherwise current limited, that sort of clearance is plenty, as long as there is absolutely no chance of anything bending and touching.
!4AWG is only 1.6mm dia. That's nowhere near what I'd call 'heavy'. However with thicker stranded wire, you do need to prepare the end carefully, especially if your iron is a bit on the wimpy side (low power or low heat capacity). Strip, immediately gently twist before the strands get disturbed from their original lay, flux the very end if its bare copper or old oxidised tin plated wire (not too much - you don't want excess flux running up under the insulation and possibly causing corrosion), and tin it, remove excess solder and trim to desired length. Then, and only then, you can solder it to a PCB pad. If you try to solder it without tinning it first, you'll have an unholy mess, probably with burnt or melted insulation for a fair way up the wire. For difficult wire tinning cases a wet tissue held round the insulation with a clothespeg can be used to heatsink it so it doesn't melt.
IMHO those blunt conical bits are only fit for
pokerwork! A chisel style (flat) tip for the Weller will make a fair bit of difference, and seldom needs to be changed for fine work - just use the corner. A hoof bit is even better for delivering heat to the joint, but can be a PITA if oversized. If the cheapo iron isn't so daggy its useless, maybe see if you can find one for it as the capability to dump 40W into larger joint will be useful.
For difficult joints in heavy wire, or with multiple wires, I reach for my Weller 8100 soldering gun. 100W of heat delivered right at the tip. However there's no temperature control and the amount of heat put into a joint is only dependent on the dwell time and how long you hold the trigger down, so until you develop a fair bit of skill with one, work on delicate boards is best avoided.