Kate Middleton and Prince William Make First Solo Outing as Prince and Princess of Wales

A new era begins for Prince William and Kate Middleton.

The senior royals, both 40, stepped out in Sandringham on Thursday to tour the 30,000 flower bouquets, balloons, notes and other tributes left by well-wishers in Queen Elizabeth's honor since her death. The outing was especially memorable because it marked the couple's first solo appearance as the new Prince and Princess of Wales. The title passed to Prince William from his father, now known as King Charles III, after the Queen "peacefully" died one week ago at age 96.

Prince William and Princess Kate spent about 45 minutes speaking with mourners gathered outside the Norwich Gates of Sandringham House.

Bex Neeve, 44, from the county of Norfolk, waited over two hours to see the couple and shared a few words with them.

"William said he thinks Monday will be hard," Neeve tells PEOPLE. "Kate said it's been overwhelming and she and William are very grateful for everyone being here. She was emotional. They seemed like they were here to soak up all the love."

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Her mother Sharon Clouting, 64, adds, "You can tell William is his mother's son. He was chatting so easily and very sincere."

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Chris Jackson/Getty Images Prince William and Kate Middleton

Sarah Tomlinson, 51, from the nearby town of Kings Lynn, came with her friend and the friend's baby.

"My friend's baby was the first jubilee baby to be born in Kings Lynn and named after Prince Louis," she says. "William came over and said how dashing he is in his outfit." The couple also "showed a real interest" in the baby and asked if he was sleeping through the night.

Samir Hussein/WireImage Prince William and Kate Middleton

She added that William also said "he thinks Paddington Bear has taken over from the corgis as being part of the royal family," following the Queen's comedy sketch with the beloved bear during the Platinum Jubilee celebrations in June.

"I can't believe how together they are — they seem to be supporting us rather than us supporting them," Tomlinson adds.

Chris Jackson/Getty Images Prince William and Kate Middleton

Kate, who wore a Catherine Walker ensemble in a nod to Princess Diana, also gave an update on how their three children — Prince George, 9, Princess Charlotte, 7, and Prince Louis, 4 — were coping.

Lydia Bailey tells PEOPLE, "Kate said the children have settled in nicely with their new school and have new friends."

Sandringham was one of two homes privately owned by the Queen, who usually spent the Christmas season there with her family. She traditionally arrived in early December and remained at the estate through February 6,  the anniversary of the day her father, King George VI, died there, making her the new monarch.

A house steeped in history, Sandringham was originally purchased by Queen Victoria and Prince Albert in 1862. Located about 110 miles north from the confines of London, a former staffer previously told PEOPLE that the Queen could truly relax at her Norfolk country home.

"She doesn't have to be monarch there," they explained. "She can be Elizabeth rather than the Queen."

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In her eldest son's first speech as monarch last Friday, he confirmed that William and Kate officially inherited the Prince and Princess of Wales titles. The Prince of Wales is traditionally held by the eldest son and heir of the reigning British monarch, his wife taking the Princess title.

Two days later, Prince William spoke to Wales' top politician, First Minister Mark Drakeford, mentioning the "deep affection" he and his wife share for Wales, where they lived as newlyweds from 2011 to 2013. They recently visited the capital city of Cardiff during the Queen's Platinum Jubilee celebrations with their two eldest children, Prince George, 9, and Princess Charlotte, 7.

Chris Jackson/Getty Images Prince William and Kate Middleton

A royal source tells PEOPLE that William and Kate are focused on "deepening the trust and respect of the people of Wales over time."

"The Prince and Princess of Wales will approach their roles in the modest and humble way they've approached their work previously," the source says.

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As Kate becomes known as the Princess of Wales, which William's mother, the late Princess Diana, once held, a royal source tells PEOPLE, "the new Princess of Wales appreciates the history associated with this role but will understandably want to look to the future as she creates her own path."