McCaw said the woman lived no more than 15 minutes from her doorstep in temporary accommodation.
"She had escaped a violent family with literally no one there to support her.
"She was entirely alone."
READ MORE: Maternal suicide: Attack on Government for 'shaming' maternal practices
McCaw said after being in hospital for two days with not one visitor her neighbour was then dropped back to the temporary accommodation on her own with her baby.
"I can't even begin to imagine the loneliness by that lack of support, especially after a c-section.
"We had vastly different experiences and based on statistics our outcomes will be different too."
McCaw wanted to encourage New Zealanders to "walk a mile in someone else's footsteps before you judge them" as part of a powerful public movement against maternal suicide.
"My nana had two weeks in hospital after giving birth, my mum had one week. Now, women are being kicked out just hours after giving birth.
"We are less connected than we have ever been."
McCaw's speech comes after decades of failed promises by Government to address New Zealand's "appalling" maternal suicide rates, which are five times worse per capita than the United Kingdom.
New Zealanders speaking at today's Parliament campaign today include science adviser Sir Peter Gluckman, wellness advocate Gemma McCaw, paediatrician Dr Johan Morreau, mum and advocate Joanne Rama, midwife Tish Tahia and founder of advocacy group Mothers Matter Chloe Wright.
Policy change
During the last election, National campaigned for a First 1000 Days policy, which was praised by advocates, including Wright, but after National failed to get into power the policy appeared to have been swept under the rug.
It included all expecting mums being entitled to at least $3000 to support their child's first 1000 days of development, with more funding available to those with high-needs.
It also included a ring-fenced DHB fund to ensure all new mums are given the option of a three-day stay at a postnatal facility after giving birth.
National MP Louise Upston, who led the proposed policy change, said it was under review but the party remained committed to pushing for the mandatory three-day postnatal stay.
Upston said once the proposed policy has been revised it would go in the Members' Bill ballot which could be drawn in a matter of days or 10 years.
"It's luck of the draw or we will consider going to Labour or the Greens for cross-party support," she said.
About maternal suicide in New Zealand:
• Every year at least 10 women are lost to maternal suicide in New Zealand - and experts say that's the "tip of the iceberg" as many go unreported. Māori and Pacifika are far less likely to report post-natal depression.
• One in seven new mums suffer postnatal depression.
• The reported rate of maternal suicide in New Zealand is five times higher per capita than that of the UK, with Māori women overrepresented.
• On average a child dies every five weeks as a result of violence in New Zealand.
Looking for support? It's available:
Call or text 1737 any time for support from a trained counsellor
Call PlunketLine 24/7 on 0800 933 922
Depression helpline: Freephone 0800 111 757
Healthline: 0800 611 116 (available 24 hours, 7 days a week and free to callers throughout New Zealand, including from a mobile phone)
Lifeline 0800 543 35
Samaritans – 0800 726 666