Aside from the recommendations about roast level and bean choice, you can adapt your brewing process a bit. Specifically, you can use a different brew ratio to change how much water passes through the puck. A longer shot, also called a lungo may have a brew ratio of about 1:3 grinds to water by mass. On the other end of the spectrum is the ristretto which may use a 1:1 ratio. A good explanation on pulling those shots by changing the grind size is found in this answer.
In your case, I think a ristretto may be what you're looking for. Because less water passes through the coffee puck, you will proportionally extract more compounds that release into the water easily. These tend to be more acidic.
As Wikipedia describes the ristretto's qualities:
A ristretto's chemical composition and taste differ from those of a full length extraction for three reasons:
- More concentrated: The first part of any extraction is the most concentrated, its color typically lying between dark chocolate and umber, whereas the tail end of shots are much lighter, varying from the color of dark pumpkin pie to varying shades of tan (see photo, above right). This is an important factor when drinking straight espresso shots.
- Different balance: Different chemical compounds in ground coffee dissolve into hot water at different rates. A ristretto contains a greater relative proportion of faster extracting compounds, proportionally fewer of the compounds characteristic of over-extraction, and thus, a different balance.
- Fewer total extracts: Relative proportions aside, fewer total coffee compounds—caffeine being just one—are extracted into ristrettos versus full length shots. This is an important factor when diluting shots into water or milk.
As an easy experiment, you could pull a regular espresso and switch cups halfway through the extraction. While that first shot won't be a balanced ristretto, comparing the two can give you an idea about the different compounds (and thus flavors) extracted at different points during the extraction process.
If you do like it, you might want to follow the advice from this answer and change your grind to get a regular extraction time (25-40 seconds) with a 1:1 brew ratio.