It is their first competitive action since the ICC World Twenty20 in March, when they beat Hong Kong to record a first win at a major tournament.
"Winning that last game against Hong Kong was pretty crucial for us," batsman Coetzer told BBC Scotland.
"Coming away with that against our name was hugely important."
That eight-wicket triumph took its time too - 21 attempts over 18 years - and the 32-year-old thinks more fixtures against higher-ranking teams like Afghanistan are vital if they are to continue building on that hard-fought success.
"The schedule is very bare at the moment and, if you are trying to produce players to compete against the top 12 nations in the world, that's going to be very hard to do if you're not playing any cricket," said Coetzer.
Scotland and Afghanistan met during the World T20 in Nagpur in March, when this week's visitors secured a 14-run victory along with qualification from the group stages, where they also beat the eventual winners West Indies.
But Coetzer believes the Scots are coming at this series, being played at The Grange in Edinburgh on Monday and Wednesday, with the strongest squad they have probably ever had.
"We've got some options with the bat and some more options with the ball now, so it's really given us a more rounded squad," said the vice-captain.
And, after that win over Hong Kong the team, led by Preston Mommsen, will be "quietly confident" they can put pressure on the visitors in what he thinks will be a "tightly contested" series.
With the temperature in Afghanistan hitting the mid-30s, Coetzer believes there could be an advantage against the team ranked 10th in the world.
"At training, they all turned up well wrapped up as it's only 13 degrees and I guess that's not what they're used to," he said.
"The pitch conditions too, the wicket may well suit our players and hopefully things like that will go in our favour - you've got to make your home ground a fortress wherever that is and that's The Grange at the minute."
Someone who has a heads-up on the disappointment of a Scottish summer is Lalchand Rajput - the former India and Scotland international who has taken charge of Afghanistan for their tour of Scotland, Ireland and the Netherlands.
The 54-year-old from Mumbai spent 10 seasons with Perthshire and another five with Strathmore and may know a thing or two about July temperatures here.
While Rajput has been quoted as calling Scotland his second home, that fondness will be swept aside as he takes the reins for the first time against the Scots, although Coetzer claims they are not expecting any massive surprises.
Having tasted success on the world stage this year, Scotland are hoping to use that to build excitement around the sport nationally.
That is perhaps hindered somewhat by the fact they do not play again until 14 and 16 August against the United Arab Emirates in Aberdeen.
"We are in a little tricky stage at the moment as our fixtures are few and far between," Coetzer told BBC Scotland. "That's the challenge we face with reducing funding from the International Cricket Council (ICC).
"It's challenging when players are trying to be professional, but you can only be together for one day leading into this series.
"That's no preparation for a one-day series, so we do have a lot of work to do in this country."
Scotland vice-captain Kyle Coetzer believes the "monkey is off their backs" when they host Afghanistan in two one-day internationals this week.