There's a lovely word, "degronching", to describe that unsticking of the clutch plates after it's sat a bit. And yes, it's a real word. I degronch every time I cold start my '05 500: just hold in the clutch, kick through the kickstarter a couple of times, and you can feel the plates give way. Doing this will make that first shift far less abrupt, difficult or "clunky".
That said, your clutch might benefit from some fine adjustment too.
When on the road, if you sometimes seem to have difficulty getting into neutral, just pull forward a foot or two in gear, and all should be well. It's just how they are and why it's a good idea to get into neutral BEFORE coming to a full stop. The one thing you don't want to do is just sit, like at a stoplight, in gear with the clutch in. This will quickly overheat the clutch and make it all "draggy".
Especially if it has sat for a long while or is just a bit "elderly", that clutch cable of yours may be a bit funky and stiff and getting ready to go "Pop!". At a minimum, you might do well to remove the cable's barrel end from the lever, inspect for any loose or broken off strands of the inner cable, orient it upright, and just drip-feed little by little a good dose of a light machine oil like 3-in-1 into it, which will feed capillary-wise down into the cable. If you have some of that white PTFE thread sealing plumbers tape, a couple of wraps of that around the cable's barrel end (the cylindrical bit) with a light smearing of grease will help make it silky smooth. It's the jarring jerky movement there that most often stresses and snaps cables. That said, though it's a bit more trouble up front, if that's an OEM cable, you'd do very well indeed to replace it with a FAR higher quality one, such as a Barnett from our Forum hosts. The Enfield ones are crap. I mean, there's a reason new bikes used to come with a spare set of them.
For what it's worth, I once described the step-by-step replacement of the cable on a 5-speed here:
https://forum.classicmotorworks.com/index.php?topic=25968.msg299048#msg299048. Your experience would be similar.