"It's such an unthinkable tragedy and the grief and trauma for him are unbearable," the source says. "Alec is still in shock and his heart is completely broken. He is doing his best to cope and is leaning on Hilaria and the kids for support."
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"Obviously, what happened here is devastating for everyone," the insider adds. "Alec will need time and space to work through and process this tragedy."
Baldwin and Hilaria, 37, share six children together, daughters Carmen Gabriela, 8, and María Lucía Victoria, 8 months, plus sons Rafael Thomas, 6, Leonardo Ángel Charles, 5, Romeo Alejandro David, 3, and Eduardo "Edu" Pao Lucas, 13 months.
He also has a 26-year-old daughter, Ireland, whom he shares with his ex Kim Basinger.
Hilaria spoke out on the incident for the first time on Monday, writing on Instagram, "My heart is with Halyna. Her husband. Her son. Their family and loved one. And my Alec."
She continued, "It's said, 'There are no words' because it's impossible to express the shock and heartache of such a tragic accident. Heartbreak. Loss. Support."
Jamie McCarthy/Getty Hilaria and Alec Baldwin
Baldwin released a statement on Twitter Friday, writing, "There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours."
"I'm fully cooperating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family," he added. "My heart is broken for her husband, their son, and all who knew and loved Halyna."
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Also on Friday, Hutchins' husband Matthew told Daily Mail that he has been in contact with Baldwin. Matthew, 38, has a 9-year-old son, Andros, whom he shared with the late cinematographer.
"I have spoken with Alec Baldwin and he is being very supportive," he told the outlet.