Not getting the creamy result beating butter and sugar

There may well be more than one issue here.

1. The type of butter. If you're using what is sometimes sold as "cooking butter" then this has a much lower moisture content than normal butter, and so it is very difficult to get the sugar to dissolve enough to cream.

2. Sugar choice. Granulated sugar is much more difficult to cream than than caster (superfine) sugar due to the large crystal size.

3. Recipe proportions. It is more common to use roughly equal weights of butter and sugar when creaming them together; here there is more than twice as much sugar compared to butter, so I am not at all surprised that it is not ending up as a very creamy mixture.

As the aim of the beating process is to dissolve the sugar and to add air, adding one of the eggs and beating well would allow you to achieve both of these.

60F that is what you need to remember. Butter need to reach 60F before you can start creaming with sugar. Colder than that is too hard. 65 is ideal, but when the hand mixer works the butter is going to get some heat. Once it is hotter than 68F you have reached point of no return. It is now waste

Disclaimer: as noted in the comments below, this technique requires a fair amount of baking experience, care, and to some degree, luck.

One helpful technique used for butter-creaming is to chop the butter into small pieces, place over a pan of softly simmering/hot water, and whisk until the butter is in a creamed state (with care taken not to melt the butter; usually the butter has to be taken off the double-boiler a few times to whisk any melted butter back into the rest if that occurs); the end result should be an opaque and thick bowl of creamed butter with a consistency ranging from a thick custard to standard, machine-creamed butter (the whisking helps retain form, and a lower temperature can help prevent the butter from getting too warm). The sugar can then be folded in until homogenous and whisked further until peaks are formed (if they have not already).

There is a fair amount of sugar in that recipe compared to butter, so creaming it may require more effort. Also, using a finer-grained sugar ("bakers'" sugar, for example) can help getting the mixture to a creamy state as the sugar crystals can more readily dissolve and dissociate into the butter; this however can require more vigorous whisking to introduce the needed air bubbles into the mixture since the finer grains of sugar will introduce less air when mixed.

This technique also comes especially handy when baking in batches that result in quantities of butter too large to cream in a standard standing mixer (and thus hand-creaming is required).