4 Digit 7 segment display flickering
With the help of Majenko and jsotola in the comments, I've got it fixed! It was the text I was displaying in the Serial Monitor that was slowing the display down. Here is the updated program that works:
#include &quot;SevSeg.h&quot;
SevSeg sevseg; 

int buttonPress{}; // Variable used in Serial monitor, simulates button press to increment counter
void setup(){
  byte numDigits = 4;
  byte digitPins[] = {10, 11, 12, 13};
  byte segmentPins[] = {9, 2, 3, 5, 6, 8, 7, 4};

  bool resistorsOnSegments = true; 

  bool updateWithDelays = false; 
  byte hardwareConfig = COMMON_CATHODE; 
  sevseg.begin(hardwareConfig, numDigits, digitPins, segmentPins, resistorsOnSegments);
  sevseg.setBrightness(90);
  Serial.begin(9600);
  sevseg.setNumber(0);
  sevseg.refreshDisplay();
}
void loop(){
  static int number = 0;
  
  if (Serial.available() &gt; 0) { // Serial monitor input for buttonPress
    buttonPress = Serial.read();
  }
// THE NEXT TWO LINES HAVE BEEN COMMENTED OUT FOR IT TO WORK
   // Serial.println(&quot;The value of buttonPress is:  &quot;);
   // Serial.println(buttonPress);
    if (buttonPress == 10){ // Increment counter if buttonPress Serial monitor input = 10
    number += 15;
    buttonPress = 0; 
    sevseg.setNumber(number); // Display the number on 4 digit 7 segment display   
    }

    sevseg.refreshDisplay(); // Refresh display
}

I'm leaving the program modifications here in case anyone else gets the same problem.