Best way is to avoid mistakes, and all of us make them. You can pick those stitches back up but not with a larger needle, it is easiest to pick them up with a smaller needle than you originally cast them onto. Go down 2 to 3 sizes or pick them up with a darning needle threaded with waste yarn. With a large cast on, it is likely you will have a few cast on stitches which will start looking terrible however.
The trouble with picking up these stitches is that many people don't see the mount of the stitch when there's nothing knit onto the stitches yet, but this mount of the stitch will look odd if you don't knit it correctly.
A small circular needle, like size 1 or 2 is fabulous to pick up your cast on. But a cast on is also quick to do. And there are other cast on methods which let you make a loose cast on which is stretchy.
Many people like to cast on over both needles to make their cast on loose. It does make knitting the first row easier. But as said above, changing to a different needles was not the way the pattern meant even though it is a way many people would interpret that. Knitters just are going to knit the next row onto the needle of your pattern as that is one of the standard abbreviations in knitting lingo.
Struggling with a section of yarn also does not let it look very pretty and you may not like what it now looks like as the stitches are fuzzier, sometimes splits the yarn.
If you use interchangeable knitting needles you change the one you are knitting onto, then when that is done, change the one now empty as I've had my stitches not be too happy the other way around.
I have decided that being happy with my final result is better than not finishing a project. It is better I fix it so that I want to finish than to say I am wasting my time and let it go.
One of my favorite cast ons is the crocheted cast on, which can be used with waste cotton yarn and can be taken out. This is handy for many reasons, as if your cast on was not loose enough, you can easily take it out and use a stretchy bind off as now you'd be knitting the other direction.
I also like the way it looks as when you slip the first stitch of the selvages, it makes a finish for the work which is identical and also identical to my cast off. Great for scarves. (Actually good for most everything) even though I use the slingshot method most of the time but I've learned how to make it loosely over the years.
If you just used hand cream, is not the time to do cast on. Hands need to be dry also and if it is humid, I have a dry wash cloth to keep my hands dry. (Even sit under a ceiling fan of use a desktop fan).
I also buy extra yarn so if I have trouble knitting with the needles I often use which is bamboo, I can experiment with other needles and as I have found that knitting a gauge swatch is not optional unless you are making an afghan, extra yarn is best to buy, and if you keep your receipt and finish the project soon enough, you can take that extra unused skein back and exchange it for something you now need.